CBSE-i X Mathematics - NIMS Dubai – N.I. Model School ... CLASS X (Core) Mathematics Surface Area...

Shiksha Kendra, 2, Community Centre, Preet Vihar,Delhi-110 092 India

CBSE-i

UNIT-14

CLASS

X

(Core)(Core)

MathematicsSurface Area and VolumeSurface Area and VolumeMathematics

Shiksha Kendra, 2, Community Centre, Preet Vihar,Delhi-110 092 India

CBSE-i

UNIT-14

CLASS

X

(Core)(Core)Surface Area and VolumeMathematics

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acknowledgements have been included wherever appropriate and

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prior permission of the CBSE-i. This material is meant for the use of

schools who are a part of the CBSE-International only.

The Curriculum initiated by Central Board of Secondary Education -International (CBSE-i) is a progressive step in making the educational content and methodology more sensitive and responsive to the global needs. It signifies the emergence of a fresh thought process in imparting a curriculum which would restore the independence of the learner to pursue the learning process in harmony with the existing personal, social and cultural ethos.

The Central Board of Secondary Education has been providing support to the academic needs of the learners worldwide. It has about 11500 schools affiliated to it and over 158 schools situated in more than 23 countries. The Board has always been conscious of the varying needs of the learners in countries abroad and has been working towards contextualizing certain elements of the learning process to the physical, geographical, social and cultural environment in which they are engaged. The International Curriculum being designed by CBSE-i, has been visualized and developed with these requirements in view.

The nucleus of the entire process of constructing the curricular structure is the learner. The objective of the curriculum is to nurture the independence of the learner, given the fact that every learner is unique. The learner has to understand, appreciate, protect and build on values, beliefs and traditional wisdom, make the necessary modifications, improvisations and additions wherever and whenever necessary.

The recent scientific and technological advances have thrown open the gateways of knowledge at an astonishing pace. The speed and methods of assimilating knowledge have put forth many challenges to the educators, forcing them to rethink their approaches for knowledge processing by their learners. In this context, it has become imperative for them to incorporate those skills which will enable the young learners to become 'life long learners'. The ability to stay current, to upgrade skills with emerging technologies, to understand the nuances involved in change management and the relevant life skills have to be a part of the learning domains of the global learners. The CBSE-i curriculum has taken cognizance of these requirements.

The CBSE-i aims to carry forward the basic strength of the Indian system of education while promoting critical and creative thinking skills, effective communication skills, interpersonal and collaborative skills along with information and media skills. There is an inbuilt flexibility in the curriculum, as it provides a foundation and an extension curriculum, in all subject areas to cater to the different pace of learners.

The CBSE has introduced the CBSE-i curriculum in schools affiliated to CBSE at the international level in 2010 and is now introducing it to other affiliated schools who meet the requirements for introducing this curriculum. The focus of CBSE-i is to ensure that the learner is stress-free and committed to active learning. The learner would be evaluated on a continuous and comprehensive basis consequent to the mutual interactions between the teacher and the learner. There are some non-evaluative components in the curriculum which would be commented upon by the teachers and the school. The objective of this part or the core of the curriculum is to scaffold the learning experiences and to relate tacit knowledge with formal knowledge. This would involve trans-disciplinary linkages that would form the core of the learning process. Perspectives, SEWA (Social Empowerment through Work and Action), Life Skills and Research would be the constituents of this 'Core'. The Core skills are the most significant aspects of a learner's holistic growth and learning curve.

The International Curriculum has been designed keeping in view the foundations of the National Curricular Framework (NCF 2005) NCERT and the experience gathered by the Board over the last seven decades in imparting effective learning to millions of learners, many of whom are now global citizens.

The Board does not interpret this development as an alternative to other curricula existing at the international level, but as an exercise in providing the much needed Indian leadership for global education at the school level. The International Curriculum would evolve on its own, building on learning experiences inside the classroom over a period of time. The Board while addressing the issues of empowerment with the help of the schools' administering this system strongly recommends that practicing teachers become skillful learners on their own and also transfer their learning experiences to their peers through the interactive platforms provided by the Board.

I profusely thank Shri G. Balasubramanian, former Director (Academics), CBSE, Ms. Abha Adams and her team and Dr. Sadhana Parashar, Head (Innovations and Research) CBSE along with other Education Officers involved in the development and implementation of this material.

The CBSE-i website has already started enabling all stakeholders to participate in this initiative through the discussion forums provided on the portal. Any further suggestions are welcome.

Vineet Joshi

Chairman

PREFACEPREFACE

ACKNOWLEDGEMENTSACKNOWLEDGEMENTS

Advisory Conceptual Framework

Ideators

Shri Vineet Joshi, Chairman, CBSE Shri G. Balasubramanian, Former Director (Acad), CBSE

Sh. N. Nagaraju, Director(Academic), CBSE Ms. Abha Adams, Consultant, Step-by-Step School, Noida

Dr. Sadhana Parashar, Director (Training),CBSE

Ms. Aditi Misra Ms. Anuradha Sen Ms. Jaishree Srivastava Dr. Rajesh Hassija

Ms. Amita Mishra Ms. Archana Sagar Dr. Kamla Menon Ms. Rupa Chakravarty

Ms. Anita Sharma Ms. Geeta Varshney Dr. Meena Dhami Ms. Sarita Manuja

Ms. Anita Makkar Ms. Guneet Ohri Ms. Neelima Sharma Ms. Himani Asija

Dr. Anju Srivastava Dr. Indu Khetrapal Dr. N. K. Sehgal Dr. Uma Chaudhry

Coordinators:

Dr. Sadhana Parashar, Ms. Sugandh Sharma, Dr. Srijata Das, Dr. Rashmi Sethi, Head (I and R) E O (Com) E O (Maths) E O (Science)

Shri R. P. Sharma, Consultant Ms. Ritu Narang, RO (Innovation) Ms. Sindhu Saxena, R O (Tech) Shri Al Hilal Ahmed, AEO

Ms. Seema Lakra, S O Ms. Preeti Hans, Proof Reader

Material Production Group: Classes I-V

Dr. Indu Khetarpal Ms. Rupa Chakravarty Ms. Anita Makkar Ms. Nandita Mathur

Ms. Vandana Kumar Ms. Anuradha Mathur Ms. Kalpana Mattoo Ms. Seema Chowdhary

Ms. Anju Chauhan Ms. Savinder Kaur Rooprai Ms. Monika Thakur Ms. Ruba Chakarvarty

Ms. Deepti Verma Ms. Seema Choudhary Mr. Bijo Thomas Ms. Mahua Bhattacharya

Ms. Ritu Batra Ms. Kalyani Voleti

English :

Geography:

Ms. Sarita Manuja

Ms. Renu Anand

Ms. Gayatri Khanna

Ms. P. Rajeshwary

Ms. Neha Sharma

Ms. Sarabjit Kaur

Ms. Ruchika Sachdev

Ms. Deepa Kapoor

Ms. Bharti Dave Ms. Bhagirathi

Ms. Archana Sagar

Ms. Manjari Rattan

Mathematics :

Political Science:

Dr. K.P. Chinda

Mr. J.C. Nijhawan

Ms. Rashmi Kathuria

Ms. Reemu Verma

Dr. Ram Avtar

Mr. Mahendra Shankar

Ms. Sharmila Bakshi

Ms. Archana Soni

Ms. Srilekha

Science :

Economics:

Ms. Charu Maini

Ms. S. Anjum

Ms. Meenambika Menon

Ms. Novita Chopra

Ms. Neeta Rastogi

Ms. Pooja Sareen

Ms. Mridula Pant

Mr. Pankaj Bhanwani

Ms. Ambica Gulati

History :

Ms. Jayshree Srivastava

Ms. M. Bose

Ms. A. Venkatachalam

Ms. Smita Bhattacharya

Material Production Groups: Classes IX-X

English :

Ms. Rachna Pandit

Ms. Neha Sharma

Ms. Sonia Jain

Ms. Dipinder Kaur

Ms. Sarita Ahuja

Science :

Dr. Meena Dhami

Mr. Saroj Kumar

Ms. Rashmi Ramsinghaney

Ms. Seema kapoor

Ms. Priyanka Sen

Dr. Kavita Khanna

Ms. Keya Gupta

Mathematics :

Political Science:

Ms. Seema Rawat

Ms. N. Vidya

Ms. Mamta Goyal

Ms. Chhavi Raheja

Ms. Kanu Chopra

Ms. Shilpi Anand

Geography:

History :

Ms. Suparna Sharma

Ms. Leela Grewal

Ms. Leeza Dutta

Ms. Kalpana Pant

Material Production Groups: Classes VI-VIII

1. Syllabus 1

2. Scope document 2

3. Teacher's Support Material 4

Teacher Note 5

Activity Skill Matrix 9

Warm Up W1 10

Dimension of Solids

Warm Up W2 11

Recalling Formulae of Solids

Pre –Content P1 12

Solids Out of Solids

Pre –Content P2 13

Which Deal is Better

Content Worksheet CW1 14

Cubes, Cuboids and Cylinders


Cones, Spheres and Hemispheres


Solid Formed by Scooping Out a Part of a Given Solid


Solids Made up of Combination of Two or More Solids


Conversion of Solids

Post Content Worksheet PCW1 20


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Contents



Assessment Plan 21

4. Study Material 26

5. Student's Support Material 44

SW1: Warm Up (W1) 45

Dimension of Solids

SW2: Warm Up (W2) 47

Recalling Formulae of solids

SW3: Pre Content (P1) 49


SW4: Pre Content (P2) 51

Which Deal is Better?

SW5: Content (CW1) 53



Cones, Sphere and Hemispheres


Solid Formed by Scooping out a Part of Given Solid





SW10: Post Content (PCW1) 86




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6. Suggested Videos & Extra Readings 92

1

Syllabus –UNIT - 14

Surface Area and Volume (Core)

Recapitulation of known formulae Formula for surface area and volume of cube, cuboid, right circular cylinder, right circular cone, sphere, hemisphere

Combination of Solids Surface area and volume of combination of solids

Conversion of solids Recasting of one solid shape into other solid shape. Application problems

2

Scope Document

Key Concepts

1. Curved Surface Area

2. Lateral Surface Area

3. Total Surface Area

4. Recasting

Learning Objective: Students will be able to

State and use the formula for lateral surface area, total surface area and volume

of cubes and cuboids, when lengths of sides are given.

State and use the formula for curved surface area, total surface area and volume

of a cylinder, when radius and height are given.

Find the surface area (TSA/CSA) of a given cube, cuboid and cylinder when

volume and some other information are given.

Find the volume of a given cube, cuboid and cylinder when surface area and

some other information are given.

State and use the formula for total surface area, curved surface area and volume

of cone, sphere and hemisphere when radius and height are given.

Find the surface area (TSA/CSA) of a given cone, sphere and hemisphere when


Find the volume of a given cone, sphere and hemisphere when surface area and


Find the surface area and volume of remaining solid when a portion of it is dug

out or cut out in shape of some other solid.

Find the surface area and volume of the obtained solid when one solid is

converted into another form by recasting.

3

Extension Activities: Students can form nets for prisms and pyramids and can derive

the formula for their lateral surface area and total surface area. Also they can establish

Euler’s Formula.

SEWA: Conduct a survey on packaging of various juices and find which of the

packaging design is best.

Research: According to one study metal available on earth is depleting very fast as the

demands of vehicles are increasing day by day.

Conduct a survey over this and prepare a report to sensitise the people to reduce the

use of individual vehicles.

4

Teacher’s Support Material

5

Teacher’s Note

The teaching of Mathematics should enhance the child’s resources to think and reason,

to visualize and handle abstractions, to formulate and solve problems. As per NCF

2005, the vision for school Mathematics includes.

1. Children learn to enjoy mathematics rather than fear it.

2. Children see mathematics as something to talk about, to communicate through,

to discuss among them, to work together on.

3. Children pose and solve meaningful problems.

4. Children use abstractions to perceive relationships, to see structures, to reason

out things, to argue the truth or falsity of statements.

5. Children understand the basic structure of Mathematics: Arithmetic, algebra,

geometry and trigonometry, the basic content areas of school Mathematics, all

offer a methodology for abstraction, structuration and generalisation.

6. Teachers engage every child in class with the conviction that everyone can learn

mathematics.

Students should be encouraged to solve problems through different methods like

abstraction, quantification, analogy, case analysis, reduction to simpler situations, even

guess-and-verify exercises during different stages of school. This will enrich the

students and help them to understand that a problem can be approached by a variety of

methods for solving it. School mathematics should also play an important role in

developing the useful skill of estimation of quantities and approximating solutions.

Development of visualization and representations skills should be integral to

Mathematics teaching. There is also a need to make connection between Mathematics

and other subjects of study. When children learn to draw a graph, they should be

encouraged to perceive the importance of graph in the teaching of Science, Social

Science and other areas of study. Mathematics should help in developing the reasoning

skills of students. Proof is a process which encourages systematic way of

argumentation. The aim should be to develop arguments, to evaluate arguments, to

6

make conjunctures and understand that there are various methods of reasoning.

Students should be made to understand that mathematical communication is precise,

employs unambiguous use of language and rigour in formulation. Children should be

encouraged to appreciate its significance.

At the secondary stage students begin to perceive the structure of Mathematics as a

discipline. By this stage they should become familiar with the characteristics of

Mathematical communications, various terms and concepts, the use of symbols,

precision of language and systematic arguments in proving the proposition. At this

stage a student should be able to integrate the many concepts and skills that he/she has

learnt in solving problems.

The unit of Surface Area and Volume has high functional aspect and is used from

packaging industry to construction and designing of aeroplanes, from biological

sciences to physical sciences. The activities designed in this unit intend to give exposure

to lots of application problems to the students as well to achieve the following learning

objectives:

• State and use the formula for lateral surface area, total surface area and volume

of cubes and cuboids, when lengths of sides are given.

• State and use the formula for curved surface area, total surface area and volume

of cylinder, when lengths of sides are given.

• Find the surface area (TSA/CSA) of given cubes, cuboids and cylinders when


• Find the volume of a given cube, cuboid and cylinder when surface area and


• State and use the formula for total surface area, curved surface are and volume of

cone, sphere and hemisphere when radius and height are given.

• Determine the surface area (TSA/CSA) of given cone, sphere and hemisphere

when volume and some other information are given.

7

• Determine the volume of given cones, spheres and hemispheres when surface

area and some other information are given.

• Determine the surface area and volume of remaining solid when a portion of it is

dug out or cut out in shape of some other solid.

• Determine the surface area and volume of the obtained solid when one solid is


• Determine the surface area and volume of frustum of cone under given

conditions.

Although the students are already familiar with all the topics covered under this unit

and have also attained a minimum level of conceptual knowledge as well as procedural

fluency, the purpose of the present unit is to give them more challenging tasks so that

they get opportunity to expand their thinking and reasoning skill.

Warm up activities are designed to help them quickly revise the known formulae as

well to provoke them to think and reflect. This will also enhance the communication

skills of students. They will start thinking loudly and will come out of fear of

mathematics and measurement.

Pre-content activities are extension activities of warm up and learners will observe that

combination of two solids give rise to new solids and will get an idea that the area and

volume of these solids can be calculated. Beauty of this unit also lies in the fact that

students learn to measure without actually measuring. They will develop the skills of

comparing the surface area and volume of two objects.

Some Content worksheets focus on MS excel sheet to let the students to explore the

comparative relation between the two solids when their one or more dimension is

changed.

In all content worksheets, exposure to lots of real life problems are given in order to

prepare them to make effective use of knowledge in life.

8

It is necessary to keep a check on student understanding of conceptual knowledge as

the lack of that often results in applying incorrect formula. Sometimes the learners

are not able to identify when to find lateral surface area and when to find curved

surface area. To overcome the problem teacher should give lots of manipulatives,

demonstrate the statement of the problems using same shaped objects and many

examples from daily life.

Lots of projects can be chosen from real life. For example to create the model of car,

ratio of 1:24 is taken in comparison to actual car. How much metal will be required to

develop the actual car?

9

Activity Skills Matrix-Surface Area and Volume

Type of Activity Name of Activity Skill to be developed

Warm UP (W1) Dimension of solids Recognition and recall

Warm UP (W2) Recalling formulae of solids Recognition and memory

Pre-content (P1) Solids out of solids Observation, thinking skills,

analytic skills

Pre-content (P2) Which is a better deal? Analytical skills and

application

Content (CW1) Cubes, cuboids and cylinders Observation, analysis,

inferential problem solving

Content (CW2) Cones, spheres and

hemispheres

Hands on, Observation,

analysis, inferential, problem

solving

Content (CW3) Solid formed by scooping out

a part of a given solid Visualizing, problem solving

Content (CW4)

Solids made up of

combination of two or more

solids

application

Content (CW5) Conversion of solids Observation, Inferential skill,

Thinking Skill, Application

Post-Content (PCW1) Assignment Problem solving skills,

Application

Post-Content (PCW2) MCQ Conceptual understanding,

Problem solving skills.

Post-Content (PCW3) Design and build a model of a

house Application

Post-Content (PCW4) Refresh your memory Memory based

10

Activity 1 – Warm Up (W1)

Dimension of Solids

Specific objective:

To recognise three dimensional objects

Description:

This is a recall exercise. Students will recognize the solids which they have already

learnt in earlier classes. Students will match the picture of the solids with their names.

Execution:

Printed worksheets may be distributed. Students will be given 5 minutes to fill their

worksheets. Cross checking may be done followed by a general discussion.

Parameters for assessment:

Able to recognise given solids.

Able to recall the names of the solids.

Extra reading:

http://www.math-salamanders.com/3-d-shapes.html

http://www.youtube.com/watch?v=ktkzgsA3HZU

http://www.youtube.com/watch?v=TeQD4IRzk2c&feature=related

http://www.math-salamanders.com/3-d-shapes.html

http://www.youtube.com/watch?v=ktkzgsA3HZU

http://www.youtube.com/watch?v=TeQD4IRzk2c&feature=related

11

Activity 2 – Warm Up (W2)

Recalling Formulae of Solids

Specific objective:

To recall formulae for surface area and volumes of 3D objects

Description:

Students have already learnt surface area and volumes of solids in class IX. This warm

up is designed for recalling the formulae of surface area and volumes of solids. Students

will play the game and will recall the formulae for playing.

Execution:

Teacher will write the names of solids, their volumes, LSA/CSA, TSA on slips and will

put them in 4 bowls. Teacher will divide the class in four groups. Students of group I

will pick up slips from bowl A, students of group II will pick up slips from bowl B,

students of group III will pick slips from bowl C and students of group IV will pick up

slips from bowl D. Students from group I will try to find the corresponding students

from group II, III and IV. Student who will search his/her partners first will win the

game.


Able to recognise given solids.

Able to recall formulae for surface area and volumes of various solids.

Extra reading:

http://thinkzone.wlonk.com/Area/AreaVol.htm


12

Activity 3 – Pre Content (PC1)


Specific objective:

To recall and draw dimensions of given solids.

Description:

This is a recall task. Students will draw various dimensions of solids such as length,

breadth and height of cuboid, radius and height of a cylinder etc. This will help

students when they will solve questions on finding surface area and volumes of these

solids.

Execution:

Printed worksheets may be distributed. Students will be given 15 minutes to fill their

worksheets. Cross checking may be done followed by a general discussion.


Able to recognise various solids.

Able to recognise and draw the dimensions of given solids.

Extra reading:

http://www.attanolearn.com/excel/cbse-10th-math-surface-areas-volumes-volume-combination-solids.jsf



13

Activity 4 – Pre Content (PC2)


Specific objective:

To introduce combination of solids

Description:

This task is designed to develop an understanding of change in surface area with the

change in shape of a solid, volume remaining the same. Teacher can extend this activity

by conducting hands on activity using sugar cubes. Ask each student to make different

shapes using 27 sugar cubes. Ask them to find the surface area of the shape formed by

them. Note the surface area told by each student on blackboard and conduct a class

discussion.

Execution:

Teacher will pose the problem in front of the students and will give 10 – 15 minutes to

the students to reflect upon their thinking in their notebooks. A general class discussion

should follow thereafter.

For the hands on activity, teacher should give 10 minutes to perform the activity and

then a class discussion should be conducted.


Able to recall surface area of a cube.

Able to recall area of a square.

Extra reading:

http://www.figurethis.org/challenges/c62/challenge.htm


14

Activity 5 – Content Worksheet (CW1)


Specific objective :

To state and use the formula for total surface area, lateral surface area and volume of cubes and cuboids, when lengths of sides are given

To state and use the formula for total surface area, curved surface area and volume of cylinder, when radius and height are given.

To find the surface area (TSA/CSA) of a given cube, cuboid and cylinder when volume and some other information are given

To find the volume of a given cube, cuboid and cylinder when surface area and some other information are given

Description:

This is a revision exercise for the students. Task 1 is designed to compare the surface

area volumes of two cylinders when the radius and height of the first is changed to

form the second cylinder. Students will perform hands on activities in groups. Each

group will make a cylinder whose radius is r and height is h with clay. They will note

down the amount of clay used to make the cylinder and the amount of paint used to

paint the cylinder. The group will repeat the same by taking radius as 2r and height as

h/2. The group will again repeat the same by taking radius as 3r and height as h/3.

Based on their activities they will observe the change in surface area and volumes of the

cylinders with the change in their radius and height.

Task 2 is the extension of task 1 and students will answer the questions given in task 2

by performing activities with clay. Task 3 contains questions related to surface area and

volumes of cube, cuboids and cylinders.

Execution:

Task 1 should be done in class in groups. Teacher will divide the class in small groups

and students will do the activity. They will fill the table provided in their notebooks.

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Task 2 can be given as home assignment followed by a class discussion.

Printed worksheets may be given for task 3.


Able to make cube, cuboid and cylinder with clay.

Able to find surface area of cube, cuboid and cylinder with given dimensions.

Able to find volume of cube, cuboid and cylinder with given dimensions.

Able to find surface area when volume and some other information is given.

Able to find volume when surface area and some other information is given.

Extra reading:

http://www.youtube.com/watch?v=SmV6i-jVcRU&feature=related

http://www.youtube.com/watch?v=Q0cmYUp3h_w&feature=related

http://www.youtube.com/watch?v=onwM_CSYlu0&NR=1

http://www.youtube.com/watch?v=Incbp5sVxXc&NR=1

http://www.ankn.uaf.edu/publications/VillageMath/cordwood.html

http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/

http://mste.illinois.edu/users/carvell/3dbox/default.html








16


Cones, Spheres and Hemispheres

Specific objective:

To state and use the formula for total surface area, curved surface area and volume

of cone, sphere and hemisphere when radius and height are given.

To find the surface area (TSA/CSA) of a given cone, sphere and hemisphere when


To find the volume of a given cone, sphere and hemisphere when surface area and


Description:

In Task 1, students will take cut outs of plane figures given in the task and will revolve

them to form 3D shapes. Teacher will explain how solids are formed when we revolve a

plain figure along its axis. For example, a right angle triangle when revolved along its

base forms a cone. They will complete the table given in the task.

Task 2 contains questions related to surface area and volumes of cone, sphere and

hemispheres.

Execution:

Task 1 will be done individually by each student and the table should be filled based on

their observation. For task 3, either the teacher can write the questions on black board

and students will solve them in their notebooks or printed worksheets may be

provided.


Able to find surface area of cone, sphere and hemisphere with given dimensions.

Able to find volume of cone, sphere and hemisphere with given dimensions.

Able to find surface area when volume and some other information are given.

Able to find volume when surface area and some other information are given.

Extra reading:

http://nlvm.usu.edu/en/nav/frames_asid_275_g_3_t_3.html

http://www.youtube.com/watch?v=NAcTBJ1boD4&feature=related



17


Solids Formed by Scooping out a Part of a Given Solid

Specific objective:

To find the surface area and volume of remaining solid when a portion of it is dug

out or cut out in shape of some other solid.

Description:

Task 1 is designed to arouse critical thinking as to what happens to the surface area and

volume of a solid when a part of it is cut out of it. Students will read the conversation

between Manju and Neelu and will take their stand and will reflect upon the same. Task

2 is based on finding the surface area and volume of remaining solid when a portion of

it is dug out or cut out in shape of some other solid

Execution:

For task 1, teacher should read out the conversation between Manju and Neelu. Teacher

may give 5 minutes for thinking and class discussion follows thereafter. Printed

worksheets may be provided for task 2. Alternatively, students can solve the problems

in their notebooks.


Able to decide whether the surface area and volume will increase or decrease or

remains same when a portion of solid is cut out.

Able to find the surface area of remaining solid when a portion of it is dug out or cut

out in shape of some other solid.

Able to find the volume of remaining solid when a portion of it is dug out or cut out

in shape of some other solid.

Extra reading:

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Solids Made Up of Combination of Two or More Solids

Specific objective:

To find the surface area and volume of solids made up of combination of two or

more solids

Description:

Task 1 is to be played on computers. This task is designed to give an insight of

formation of solids. In task 2, students will find surface area and volumes of solids

formed by combination of cubes. Task 3 is a question framing task in which students

will observe the pictures and will frame questions based on their understanding. Task 4

contains questions based on solids formed by joining two or more solids.

Execution:

Task 1 is to be done in computer lab. Students can work individually or in pairs to do

these tasks. For task 2 and 3, printed worksheets may be provided. Task 4 may be done

in the notebooks followed by a class discussion.


Able find the surface area of solids made up of combination of two or more solids.

Able find the volume of solids made up of combination of two or more solids.

Extra reading:

http://www.excellup.com/classten/mathten/areavolumeexone.aspx

http://www.excellup.com/classten/mathten/areavolumeextwo.aspx

http://www.youtube.com/watch?v=l5tJ9JocFFM&feature=related




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Specific objective:

To find the surface area and volume of the obtained solid when one solid is


Description:

Task 1 is designed to make students understand that the volume of a solid remains

same when it is converted from one solid shape to another. Students will make various

solids with the same amount of clay. In task 2 students will measure the dimensions of

the solids made by them and will find their surface area and volumes. Task 3 is to solve

questions based on surface area and volume of the obtained solid when one solid is


Execution:

Task 1 is to be conducted in groups. Each group will make solids with clay and will

note down their dimensions. Task 2 may be done in notebooks. A follow up class

discussion should be conducted. For task 3, printed worksheets may be distributed.


Able to find the surface area of obtained solid when one solid is converted into

another form by recasting

Able to find volume of the obtained solid when one solid is converted into another

form by recasting

Extra reading:

http://www.youtube.com/watch?v=OAotjwOKpQs&feature=related


20

Activity 10- Post Content (PCW1)

Students will be assessed on the worksheet containing questions on finding surface

areas and volumes.


Students will be assessed on the worksheet containing MCQ on surface area and

volumes of solids.


Students will be assessed on a project work to de done in groups. They will make

design and build model of a house.


Students will be assessed on the worksheet containing questions based on formulae

used in the complete chapter.

21

Assessment Plan

Assessment Guidance Plan for Teachers

With each task in student support material a self-assessment rubric is attached for

students. Discuss with the students how each rubric can help them to keep in tune their

own progress. These rubrics are meant to develop the learner as the self motivated

learner.

To assess the students’ progress by teacher two types of rubrics are suggested below,

one is for formative assessment and one is for summative assessment.

Suggestive Rubric for Formative Assessment (exemplary)

Parameter Mastered Developing Needs

motivation

Needs personal

attention

Determine the

surface area

and volume of

given solid.

• Able to find

the surface

area and

volume of

cube and

cuboid when

the length of

edges are

given.

• Able to find

the surface

area and

volume of

cylinder and

cone when

the radius

and height

are given.

• Able to find

the surface

area and

volume of

cube and

cuboid when

the length of

edges are

given .

• Able to find

the surface

area and

volume of

cylinder,

and cone are

given when

the radius

and height

are given.

• Able to state

the surface

area and

volume of

cube and

cuboid when

the length of

edges are

given but

can not find

it accurately.

• Able to state

the surface

area and

volume of

cylinder, and

cone are

given when

the radius

and height

are given but

not able to

find it

accurately.

• Not able to

state the

surface area

and volume

of cube and

cuboid when

the length of

edges are

given.

• Not able to

state the

surface area

and volume

of cylinder,

and cone are

given when

the radius

and height

are given.

22

• Able to find

the surface

area and

volume of

sphere and

hemisphere

when the

radius is

given.

• Able to find

the surface

area when

volume of

solid and any

other

conditions

given.

• Able to find

the volume

when the

surface area

and any

other

condition is

given.

• Able to find

the surface

area and

volume of

sphere and

hemisphere

when the

radius the

radius is

given.

• Not able to

find the

surface area

when

volume of

solid and

any other

conditions

given.

• Not able to

find the

volume

when the

surface area

and any

other

condition is

given.

• Able to state

the surface

area and

volume of

sphere and

hemisphere

when the

radius is

given.

• Not able to

find the

surface area

when

volume of

solid and

any other

conditions

given.

• Not able to

find the

volume

when the

surface area

and any

other

condition is

given.

• Not able to

state the

surface area

and volume

of sphere

and

hemisphere

when the

radius is

given.

• Not able to

find the

surface area

when

volume of

solid and any

other

conditions

given.

• Not able to

find the

volume

when the

surface area

and any

other

condition is

given.

From above rubric it is very clear that

• Learner requiring personal attention is poor in concepts and requires the training

of basic concepts before moving further.

• Learner requiring motivation has basic concepts but face problem in calculations

or in making figures. He can be provided with remedial worksheets.

• Learner who is developing is able to choose suitable method of solving the

problem and is able to get the required answer too. May have the habit of doing

23

things to the stage where the desired targets can be achieved, but avoid going

into finer details or to work further to improve the results. Learner at this stage

may not have any mathematical problem but may have attitudinal problem.

Mathematics teachers can avail the occasion to bring positive attitudinal changes

in students’ personality.

• Learner who has mastered has acquired all types of skills and need more

challenging problems.

24

Teachers’ Rubric for Summative Assessment of the Unit

Parameter 5 4 3 2 1

Surface Area

and Volume

• Able to find the lateral

surface area, total surface

area and volume of cube

and cuboid of given

dimension correctly.

• Able to find the curved

surface area, total surface

area and volume of

cylinder and cone of

given dimension

correctly.

• Able to find the total

surface area and volume

and sphere and

hemisphere of given

radius correctly.

• Able to solve related

problems based on real

life situations.

• Not able to find the

lateral surface area, total


of cube and cuboid of

given dimension.


curved surface area, total


of cylinder and cone of

given dimension.

• Not able to find the total


of sphere and

hemisphere of given

radius.

• Not able to solve related


life situations.

Combination

of solids

• Able to find surface area

and volume of solids

obtained by combining

two or more shapes.

• Able to find the surface

area and volume of solid

obtained when one solid

is cut out from another.



life situations.

• Not able to find surface

area and volume of

solids obtained by

combining two or more

shapes.



of solid obtained when

one solid is cut out from

another.



life situations.

Conversion

of solids

• Able to understand that

volume of solid remains

same when recasted from

one shape to another, but

• Not able to understand

that volume of solid

remains same when

recasted from one shape

25

surface area may or may

not remain same.

• Able to find the surface

area or unknown

dimension when one

solid is converted into

other.



life situations.

to on other, but surface

area may or may not

remain same.


surface area or unknown

dimension when one

solid is converted into

other.



life situations.

26

STUDY

MATERIAL

27

SURFACE AREA AND VOLUME (CORE)

INTRODUCTION

You are already familiar with some solid figures such as a cuboid, cube, right circular

cylinder, right circular cone, sphere, hemisphere.

You have also studied finding their surface areas and volumes.

In this unit, we shall first review these concepts and extend this knowledge to study

surface areas and volumes of some more solid figures formed by combination of these

solids.

1 Recapitulation of Surface Areas and Volumes of known solids

Look at the solid (Fig 1(i)).

It is a cuboid.

Its total surface area = 2 (

Lateral surface area = 2 ( + b) h and sq. units and

Volume = b h cu units

Look at the solid (Fig1 (ii))

It is a cube of side (edge) a

Its total surface area = 6a2 sq units

Lateral surface area = 4a2 sq units and

Volume = a3 cu units

Look at the solid (Fig 1 (iii)).

It is a right circular cylinder.

Its curved lateral surface area = 2 rh sq units

Total surface area = 2 r(h + r) sq units

Volume = r2h cu. units

28

Look at the solid (Fig 1 (iv)).

It is a right circular cone.

Its curved (lateral) surface area = r sq units, where

Total surface area = r( +r) sq units, and

Volume = r2h cu units

Look at the solid (Fig 1 (v)).

It is a sphere

Its surface area = 4 r2 sq units,

Volume = r3 cu units

Look at the solid (Fig 1 (vi)).

It is a hemisphere

Its curved surface area = 2 r2 sq units,

Total surface area =3 r2 sq units, and

Volume = r3 cu units Fig. 1

Example 1: Length, breadth and height of a cuboid are 13cm, 5cm and 2cm respectively.

Find its

(i) total surface area (ii) lateral surface area and

(ii) volume.

Solution: Here 13 cm, b = 5 cm and h = 2 cm

(i) Total surface area of the cuboid

= 2( b + bh + h)

= 2 (13 x 5 + 5 x 2 + 13 x 2) cm2

= 2 (65 + 10 + 26) cm2

= 202 cm2

29

(ii) Lateral surface area of the cuboid

= 2 ( +b) h = 2 (13 +5) x 2

= 72 cm2

(iii) Volume of the cuboid = bh

= 13 x 5 x 2 cm2

= 130 cm3

Example 2: Side of a cube is 7 cm. Find its

(i) total surface area , (ii) lateral surface area and

(ii) volume

Solution: (i) Total surface area of the cube = 6a2 = 6 x 7 x 7 cm3 = 294 cm3

(ii) Lateral surface area = 4a2 = 4 x 7 x 7 cm2 = 196 cm2

(iii)Volume = a3 = 7 x 7 x 7 cm3 = 343 cm3

Example 3 : Capacity of cylindrical vessel of height 1 metre, open at the top, is 15.4

litres. Find the area of the metal sheet used in making it. (use )

Solution : Volume of the cylindrical vessel

= 15.4 litres

= 15.4 x 1000 cm3

Let r be the radius of the vessel.

Then Volume = r2h = 15.4 x 1000

x r2 x 100 = 15.4 x 1000 [ 1 m = 100 cm]

r2 = x x

= 49

r = 7cm

Area of the metal sheet used = 2 rh + r2

= 2 x x 7 x 100 + x 7 x 7 cm2

= (4400 + 154) cm2

30

= 4554 cm2

= 0.4554 m2

Example 4: Volume of a right circular cone is 78848 cm3. Its radius is 28 cm. Find its

(i) curved surface area and

(ii) total surface area

Solution: Here base radius (r) = 28 cm.

Volume = 78848 cm3

So r2h = 78848

or x x 28 x 28 x h = 78848

h =

= 96 cm

Slant height =

= cm

= cm

= 100 cm

(i) Curved surface area of the cone

= r

= x 28 x 100 cm2

= 8800 cm2

(ii) Total surface area of the cone = r + r2

= 8800 + x 28 x 28 cm2

= (8800 + 2464) cm2

= 11264 cm2

Example 5: Total surface area of a hemisphere is 462cm2. Find its volume.

Solution: Let the radius of the hemisphere be r.

31

Total surface area = 462cm2

So, 462 = 3 r2 = 3 x r2

r2 =

r2 = 49

r = 7 cm

Thus, Volume of the hemisphere = r3

= x 7 x 7 x 7cm3

= 718.67cm3 (approx)

2. Combination of Solids

So far, we have discussed surface areas and volumes of single known solids only.

But in our daily life, we come across solids which are made up of two or more of

these solids.

For example, see some solids in [Fig2. (i) to (iv)]

32

Fig.2

Each of the above solids is a combination of known solids such as cuboid, cylinder,

cone, hemisphere etc.

Many a times, we need to find surface areas and volumes of such solids.

We explain the process of finding surface areas and volumes of such through some

example.

Example 6: A toy is in the shape of a cone surmounted by a hemisphere as shown in

Fig3. Radius of each of cone and the hemisphere is 5cm and the total height of the toy is

17cm. Find

(i) total surface area, and

(ii) volume of the toy.

Solution:

Total surface area of the toy

= Curved surface area of conical part + Curved surface area of

hemispherical part.

To find curved surface area of conical part

Here r = 5cm, h = height of cone = 17cm – 5cm = 12cm

So, slant height =

33

= cm

= cm

= cm

= 13 cm.

Thus, CSA = r

= . 5. 13 = 65 cm2

To find curved surface area of hemispherical part

r = 5cm.

So, CSA = 2 r2 = 2 (5)2 = 50

From (1), total surface area of the toy = 65 + 50 = 115

Observe that total surface area of the toy is less than the sum of total surface area of the

cone and total surface area of the hemisphere!!

(ii) Volume of the toy

= Volume of conical part + Volume of hemispherical part.

= r2h + r3

= (52) (12) + . 5 x 5 x 5

=

Observe that volume of the toy is the same as the sum of volumes of cone and

hemisphere!

Example 7: A circus tent is cylindrical upto a height of 4.2 m and conical above it. The

common diameter of the base of cylindrical and conical parts is 6m.

If the total height of the tent from the ground is 8.2m, find the cost of canvas needed to

make the tent at the rate of Rs 160 per m2.

Solution: (See Fig 4)

Height of conical part

= Total height of the tent

34

Height of cylindrical part

= (8.2 – 4.2) m = 4m.

Slant height of conical part =

= m

= 5m.

Canvas needed to make the tent

= Curved surface area of cylindrical part + Curved surface

area of conical part

= 2 rh + r

= 2. . 3. (4.2) + . (3) (5) = (79.2 + 47.1) m2 approx

= 126.3 m2

Cost of the tent at the rate of Rs160/m2 = Rs (126.3 x 160) = Rs.

20208

Example 8: A godown is in the shape of a cuboid surmounted

by a half cylinder as shown in Fig 5. Find (i) its capacity and

(ii) the cost of painting it inside except the front rectangular

gate at the rate of Rs. 50/m2 (use = 3.14)

Solution :

(i) Capacity of godown

= Volume of cuboidal part + Volume of half cylindrical part

= bh + r2h

= [(15 x 8 x 10) + (3.14) (4)2 (15)] m3 [Note that diameter = 8m

Height of cylindrical part

= length of cuboidal part]

= (1200 + 376.8)m3

= 1576.8 m3

(ii) Inner surface area of the godown excluding the gate

= Area of 3 walls of the cuboid

m

35

+ (Total curved surface area of the cylinder)

= 2 (15 x 10) m2 + (10 x 8) m2 + [(2 2 r2]

= 380m2 + [(3.14) (4) (15) + (3.14) (4)2] m2

= 380 m2 + (188.40 + 50.24) m2

= 618.64 m2

Thus, cost of painting = Rs. 618.64 x 50 = Rs 30932

Example 9: An oil tanker is in the shape of a cylinder with hemispherical ends as shown

in Fig. 6. If the diameter each of cylinder and hemisphere is 1.4 m, find

(i) capacity of the tanker, and

(ii) the amount of metal sheet required to make the tankers (use ).

Solution

Note that this solid is a combination of two hemispheres and one cylinder. Here

r = 0.7m (Why?)

So, (i) required capacity = r3 + r2h + r3

= r3 + r2h

= m3

= (1.437 + 6.468) m3

= 7.905m3

=7905000 cm3 = 7905 litres

(ii) Metal used = Curved surface area of two hemispheres + Curved surface area of the

cylinder

= 2 r2 + 2 r2 + 2 rh

= 4 r2 + 2 rh

36

= [4 x x 0.7 x 0.7 + 2 x x 0. 7 x 4.2]m2

= (6.16 + 18.48) m2

= 24.64 m2

Example 10 : From a solid cylinder of height 24cm and radius 7cm, a conical cavity of

the same height and same radius is taken out. Find

(i) the volume of remaining solid, and

(ii) total surface area of the remaining solid. (use )

Solution: See Fig 7. Here r = 7cm, h=24cm.

(i) Volume of the remaining solid

= Volume of cylinder - Volume of cone

= r2h – r2h

= r2h = x x 7 x 7 x 24 cm3

= 2464 cm3

(ii) Total surface area of the remaining solid

= Curved surface area of the cylinder

+ Area of base (bottom) of the cylinder

+ Curved surface area of the conical cavity.

= 2 rh + r2 + r

= (7) [2 x 24 + 7 + 25] cm2 [ = = = = 25cm]

= 22 (48 + 7 + 25) cm2

= 1760 cm2

Example 11: A toy rocket is in the shape of a cylinder surmounted by a cone as shown

in Fig.8. The radii of the cylinder and cone are 2cm and 5cm respectively. The total

height of the toy is 42cm. Find the total surface area of the toy. (use )

37

Solution: See Fig 8.

Height of the cylinder = 42 cm – 12cm = 30cm

Radius of cone (r2) = 5cm

Radius of base of the cylinder (r1) = 2cm

Note : is also the radius of the smaller circle in the cone base

Total surface area of the toy = Curved surface area of cylinder +

Area of base of cylinder + Curved surface area of cone

+ Area of base of cone

– Area of base of cylinder

= 2 r1h + 2

1r + + 2

2r - 2

1r

= 2 r1h + r2 + 2

2r , where is the slant height of the cone.

= 2. . 2 (30) + (5) (13) + . 5 x 5

2 2

2 2

= h + r

(12) + (5)

= 169 = 13cm

= 120 + 65 + 25

= 210 = 210 x = 660 cm2

3. Conversion of Solids

Many a times, we need to convert a solid into another solid of the different or of the

same shape. For example, a metallic sphere is converted to form a wire (cylindrical

shape), a cuboidal block to a sphere or a big sphere to small spheres (lead shots etc.).,

the earth dug out from a well to form an embankment (cylindrical shape) etc.

The basic idea behind solving such problem involves equality of volumes of two

objects.

However, in such cases, the surface area of the resulting solid/solids may not be the

same.

Let us explain this through some example.

38

Example 12: The radius of a metallic spherical ball is 3cm. It is melted and recast into

spherical balls each of radius 0.75cm. Find the number of small balls so formed.

Solution: Volume of original metallic ball

= 3 = (3)3 cm3

Volume of a small ball = r3 = (0.75)3 cm3

Let the number of small ball be x

So, volume of small balls = x x ( (0.75)3) cm3

Now, x x (0.75) (0.75) (0.75) = x 3 x 3 x 3

x = = 64

Hence, the number of small balls = 64

Example 13: A cone of height 48cm and base radius 12cm is made up of modelling clay.

It is dismantled and reshaped into a sphere. Find the surface area of the sphere.

Solution: Volume of cone = r2h

= . 12 x 12 x 48cm3

Let R be the radius of the sphere. Then

its volume = R3

Now, R3 = x x 12 x 12 x 48

R3 = (12)3

R = 12

Thus, radius of the sphere = 12cm.

Now, the surface area of the sphere = 4 r2 = 4 x x 12 x 12 = 1810.3 cm3 (approx)

Example 14: A copper rod of radius 0.5cm and length 8cm is drawn into a wire of

uniform thickness cm. Find the length of the wire.

Solution: Volume of rod = r2h = (0.5) (0.5) (8)cm3

Let the length of wire be x cm

39

Note that wire is also a cylinder.

Radius of wire = ( cm) = cm.

Volume of wire = r2h = ( ) ( ) x

So, ( ) ( ) x = (0.5) (0.5) (8)

x = 0.5 x 0.5 x 8 x 30 x 30

= 1800cm

So, the length of wire = 18m

Example 15: Water is flowing at the rate of 2.5km per hour through a cylindrical pipe of

radius 7cm into a rectangular tank of length 25m and 22m wide. Determine the time in

which the level of water in the tank will rise by 35cm.

Solution:

Let the time required for the pipe to raise the water in the tank by 35cm be x hours

Volume of water flowing through the pipe in one hour = r2h

= x x x 2500 m3

[Radius = 7cm = m)

= m3

In x hours water following through the pipe = x m3 (1)

Volume of water in the tank after x hours = Volume of the cuboid of length 25m and

breadth 22m and height 0.35m.

= x b x h

= 25 x 22 x 0.35m3 (2)

From (1) and (2)

x = 25 x 22 x

x = 25 x 22 x x = 5

So required time = 5 hours

40

Example 16: A well of diameter 3.5m is dug 12m deep in a rectangular field of

dimensions 28m x 22m. The earth taken out of it is evenly spread on the remaining part

of the field. Find the height by which the level of field will be raised. (use )

Solution:

Volume of earth dug out

= r2h = (1.75) (1.75) (12)m3

Area of field on which the earth will be spread = (28m x 22m) – (1.75)2 (Why ?)

Let the level of field raised = x m.

So, x [ 28 x 22 – (1.75)2] = (1.75) (1.75) (12)

x = 2

221.75 1.75 12

722

28 1.757

x 22

=

231

277

616 8

= x =

So, the level of the field will be raised by 19 m.

Example 17: A metallic box in the shape of solid cuboid has dimensions

100cm x 50cm x 25cm. It is recast into a solid cube. Find the difference of surface areas

of two solids.

Solution:

Volume of the box = 100 x 50 x 25 cm3

Let the edge of the cube so formed be x cm.

So, x3 = 100 x 50 x 25

= 125000 = (50)3

x = 50

41

Surface area of the box = 2 (100 x 50 + 50 x 25 + 100 x 25) cm2

= 17500 cm2

Surface area of the cube = 6 x (50)2 = 15000 cm2

Difference = (17500 – 15000) cm2 = 2500 cm2

Example 18: A well of inner diameter 7 m has been dug 7 m deep and the earth dug out

is used to form an embankment 4.5 m wide around it. Find the height of the

embankment.

Solution:

Let r be the radius of the well. (See Fig.9)

Then r = 3.5 m

Volume of earth dug out

= r2h = x (3.5) (3.5) (7) m3 [As depth h = 7 m]

= x x x 7 = m3

Outer radius (R) of embankment = 3.5m + 4.5m = 8 m

Area of the base of embankment = Outer circle area – Inner circle area

= (R2 – r2) = (R + r) (R - r)

= (8 + 3.5) (8–3.5) m3

= (11.5) (4.5) m3 = m3

Height of embankment =

=

=

539

22277

14

m

= 1.66 m approx.

42

Example 19: A cylindrical bucket 40 cm high has base radius 36 cm. It is completely

filled with sand. Then it is emptied on the ground forming a conical heap of height

30 cm. Find the radius of the heap and also its curved surface area.

Solution: Radius (r) of the bucket = 36 cm

Height (h) = 40 cm

Volume of sand in bucket = r2h

= (36) (36) (40) cm3 (i)

Let r1 be the radius of conical heap of sand.

Height of conical heap = 30 cm

Volume of conical heap = 2

1r h

= 2

1r x 30 cm3

= 102

1r (ii)

From (i) and (ii),

Volume of conical heap of sand = Volume of sand in bucket

10 = (36) (36) x 40

= (36) (36) (4)

r1 = 36 x 2 = 72

Thus, radius of conical heap of sand = 72 cm

Slant height of the heap =

= cm

= cm = 78 cm

Therefore, curved surface area of the heap = r1

= x 72 x 78 cm2

= 5616 cm2

Example 20: A solid copper sphere of radius 4.9 cm is melted and recast into a solid

cylinder of diameter 14 cm. Find the curved surface area of the cylinder so formed.

Solution: Volume of sphere = r3

43

= (4.9)3 cm3

Let h be the height of the cylinder formed.

Radius of cylinder (r) = = 7 cm.

Since, Volume of sphere = Volume of cylinder formed

So, (4.9)3 = (7)2 h

h = .

h = . = 3.20 cm approx

Curved surface area of the cylinder

= 2 rh

= 2 x x 7 x 3.20 cm2

= 140. 8 cm2 approx

44

Student’s Support Material

45

Student’s Worksheet 1

Warm Up (W1)

Dimension of Solid

Name of Student_______________ Date___________

Make the dimensions of the solids given below and indicate the symbols against each.

Solids Names

h = height

r = radius

46

Self Assessment Rubric 1 – Warm Up (W1)

Parameter

Able to recognise given

solids.

Able to recall the names

of the solids.

47


Warm Up (W2)

Recalling Formulae for Solids

Name of Student_______________ Date_____________

Game: Complete the chain

Bowl A contains slips having names of the solids you learnt in earlier classes. Bowl B

contains slips on which formulae of volumes of these solids are written. Bowl C

contains slips on which formulae of lateral/curved surface area of these solids are

written. Bowl D contains slips on which formulae of total surface area of these solids are

written. Divide your class in four groups. Students of group I will pick up slips from

bowl A, students of group II will pick up slips from bowl B, students of group III will

pick slips from bowl C and students of group IV will pick up slips from bowl D.

Students from group I will try to find the corresponding students from group II, III and

IV. Student who will search his/her partners first will win the game.

Bowl A Bowl B

Bowl C Bowl D

48

Self Assessment Rubric 2 – Warm Up (W2)

Parameter

Able to recognise given

solids.

Able to recall formulae

for surface area and

volume of various solids.

49


Pre Content 1 (PC1)



Devya made a cube from 27 small cubes. Monika made 2 solids from 27 small cubes as

shown. Both of them used same sized small cubes.

Monika’s Solids Devya’s Solid

They want to paint their solids. Who will need more paint?

Try it yourself and find out.

50

Self Assessment Rubric 3 – Pre Content (PC1)

Parameter

Able to recall surface area

of a cube.

Able to recall area of a

square.

51


Pre Content 2 (PC2)



Karuna and Rajat went to an ice cream parlour and purchased same flavour ice creams.

Karuna bought ice cream (in a plastic cone of radius 3.5 cm and height 7 cm) for Rs. 20.

Rajat bought ice cream (in a plastic cylinder for height 7 cm and 3.5 cm) for Rs. 20.

Which is a better deal? Why?

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

52

Self Assessment Rubric 4 – Pre Content (PC2)

Parameter

Able to recall volume of a

cone.

Able to recall volume of a

cylinder.

53


Content Worksheet (CW1)

Cubes, Cuboids and Cylinders Name of Student_______________ Date_____________

Task 1: Activity

Relation between volumes and surface area of two cylinders when the radius of new

cylinder is n times the radius of the original cylinder and height is of the original

cylinder.

Divide the class in small groups of 5 to 6 children each.

Each group will perform the following activity.

With the help of clay, make a cylinder whose radius is r and height is h. Note down the

amount of clay used. Paint the cylinder. Note the amount of paint used.

Now make another cylinder such that its radius is 2r and height is h/2. Again, note the


54

Now make another cylinder such that its radius is 3r and height is h/3. Again, note the


Now, complete the following table.

Gro

up

s

Rad

ius

( r

)

Heig

ht

(h)

Am

ou

nt

of

clay

use

d

Am

ou

nt

of

pain

t

use

d

Rad

ius

(2r

)

Heig

ht

(h

/2)

Am

ou

nt

of

clay

use

d

Am

ou

nt

of

pain

t

use

d

Rad

ius

(3r

)

Heig

ht

(h/3

)

Am

ou

nt

of

clay

use

d

Am

ou

nt

of

pain

t

use

d

Group 1

Group 2

Group 3

Group 4

Group5

Group 6

Observe the above table carefully. Do you see any relation between the amounts of clay

used in the three cylinders made? Is there any relation in the amount of paint used to

paint the three cylinders?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Based on the above observation, comment on the following statements:

55

The volume of a cylinder becomes n times if its radius becomes n times and its height becomes

nth times.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

The surface area of a cylinder remains the same even if its radius becomes n times and its

height becomes nth times.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

Task 2:

Perform the above activity to find out how the volume and surface area changes with

the change in the dimensions of the solids given below:

Cone

Sphere

Hemisphere

You may refer:

Nets (3D model) Generator: http://www.senteacher.org/wk/3dshape.php

http://www.senteacher.org/wk/3dshape.php

56

Task 3 : Do the questions given below:

1. If the length of each edge of a cube is tripled, what will be the change in its volume?

What will be the new surface area?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

2. A carpenter makes a box which has a volume of 13400 cu. cm. The base has an area

of 670 sq. cm, what is the height of the box? What is the total surface area of the box.

57

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

3. A cuboidal tin open at the top has dimensions of 20 cm X 16 cm X 14 cm. What is the

total area of a sheet of metal required to make 10 such tins?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

4. A hollow garden roller 42 cm wide with a girth of 152 cm is made of cast iron 2 cm

thick. Find the volume of iron.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

58

5. The circumference of the base of a right circular cylinder is 176 cm and it is 1 m high.

Find the lateral surface area of the cylinder.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

6. The radius and height of a cylinder are in the ratio 3 : 2 and its volume is 2772 cu. cm.

Find its radius and height. Also, find its curved surface area and total surface area.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

7. The diameter of a roller is 80 cm and its length is 126 cm. It takes 750 revolutions to

level a playground. Find the area of the playground.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

8. The walls and ceiling of a room are to be plastered. The length, breadth and height of

the room are 4.5m, 3m, and 350 cm respectively. Find the cost of plastering at the rate of

Rs 8 per sq. m

______________________________________________________________________________

______________________________________________________________________________

59

______________________________________________________________________________

______________________________________________________________________________

9. 432 cm2 of cardboard is needed to make a cuboidal box which is 8 cm wide and 6 cm

high. Find the breadth of the box. Also, find its volume.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

10. Find the volume of a rectangular solid, each of whose side, front and bottom faces have

an area equal to 12 cm2, 8 cm2 and 6 cm2 respectively.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

11. The length, breadth and height of a cuboid are in the ratio 7 : 4 : 3 respectively. If the

whole surface of the cuboid is 1098 cm2, find its dimensions. Also, find its volume.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

12. 10 cylindrical pillars of a building have to be cleaned. The diameter of each pillar is 50

cm and the height 4 m. Calculate the cost of cleaning all the pillars at the rate of Rs. 5

per sq. m.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

60

Self Assessment Rubric 5 – Content Worksheet (CW1)

Parameter

Able to make cube, cuboid and

cylinder with clay.

Able to find surface area of cube,

cuboid and cylinder with given

dimensions.

Able to find volume of cube,

cuboid and cylinder with given

dimensions.

Able to find surface area when

volume and some other

information is given.

Able to find volume when surface

area and some other information

is given.

61



Cones, Spheres and Hemishperes


Task 1:

Cut the plane figure given below. Revolve the figures along the vertical axis and the

horizontal axis. Fill the table based on your observations.

Plane figure Draw the

solid

obtained

by

revolving

along

vertical

axis

Name of 3D solid

generated

Measures of

dimensions

Volume

Surface area

Draw the

solid

obtained

by

revolving

along

horizontal

axis

Name of 3D solid

generated

Measures of

dimensions

Volume

Surface area

Solid obtained is

______

r = ……., h = ………

Volume = …………..

Total Surface Area =

…………….

Solid obtained is

______

r = ……., h = ………



…………….

Solid obtained is

______

r = ……., h = ………



…………….

Solid obtained is

______

r = ……., h = ………



…………….

Solid obtained is

______

r = ……., h = ………



…………….

Solid obtained is

______

r = ……., h = ………



…………….

62

Task 2 : Do the following

1. How many meters of cloth 5m wide will be required to make a conical tent, the

radius of whose base is 7m and whose height is 24m?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

2. The radius of a sphere is 7cm. If the radius be increased by 50%, find by how much

percent its volume is increased.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

3. The internal and external diameters of a hollow hemispherical vessel are 24cm and

25cm respectively. If the cost of painting 1cm2 of the surface area is Rs. 5.25, find the

total cost of painting the vessel all over

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

4. The volume of a vessel in the form of a right circular cylinder is and its

height is 7cm. Find the radius of its base. Also, find its curved surface area and total

surface area.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

63

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

5. A closed iron tank with the dimensions 12 m x 9 m x 4 m is manufactured.

Determine the cost of iron sheets used at the rate of Rs. 5 per metre. (The sheet is 2 m

wide).

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

6. How many metres of cloth 1.1m wide will be required to make a conical tent whose

vertical height is 12cm and base radius is 16m? Find also the cost of the cloth used at

the rate of Rs. 14 per metre.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

_________________________________________________________________________

7. A right circular cone of height 4 cm has a curved surface area 47.1 cm2. Find its

volume.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

8. If the surface area of a sphere is 616cm2, find its volume.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

64

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

9. The circumference of the edge of a hemispherical bowl is 132cm. Find the capacity of

the bowl.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

10. A cone and a hemisphere have equal bases and equal volumes. Find the ratio of

their heights.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

65


Parameter

Able to find surface area

of cone, sphere and

hemisphere with given

dimensions.

Able to find volume of

cone, sphere and

hemisphere with given

dimensions.

Able to find surface area

when volume and some

other information are

given.

Able to find volume

when surface area and

some other information

are given.

66



Solids Formed after Scooping Out a Part of a Given Solid

Name of Student __________________ Date_____________

Task 1: Manju and Neelu are doing their math homework on surface area and volumes.

Read their conversation carefully.

Manju: Whenever we scoop out a solid from another solid, the surface area and volume

of the new solid thus formed is always less than the original solid.

Neelu: I don’t agree Manju. I think only the volume will be less.

Manju: But we are taking out some amount of solid, why will the surface area not

decrease?

Reflect your views on the above discussion.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Task 2: Do the following

1. A plot of land measures 240 m x 180 m. A trench, 10 m wide, is dug around it. The

earth dug out is spread evenly over the plot. This raises the level of the plot by 25

cm. Find the depth of the trench.

67

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

2. Find the area to be painted in the following box with a cylindrical hole. Given

that length = 15 cm, width = 12 cm, height = 20 cm and radius = 3 cm.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

68

3. How many cubic metres of earth must be dug to sink a well 7 metres deep and

diameter 28 m?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

4. The dimensions of a field are 160 m x 130 m. A pit is dug in the field, which is 40

m long, 20 m wide and 4 m deep. The earth removed is spread over the remaining

area of the field. Calculate the level of the field raised.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

5. A well is dug 20 m deep. Its diameter is 14 m. The earth dug out is spread evenly

to form a platform 22 m x 14 m. Determine the height of the platform.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

69

6. The largest sphere is carved out of a cube of side 7cm. Find the volume of the

sphere.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

7. A cylinder is 14 cm in length. The difference between the inside and the outside

surfaces of this cylinder is 88 cm2. If the volume of the cylinder is 176 cm3,

calculate its inner and outer radii.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

70


Parameter

Able to decide whether

the surface area and

volume will increase or

decrease or remains same

when a portion of solid is

cut out.

Able to find the surface

area of remaining solid

when a portion of it is

dug out or cut out in

shape of some other solid.

Able to find the volume

of remaining solid when a

portion of it is dug out or

cut out in shape of some

other solid.

71




Name of Student __________________ Date_____________

Task 1: Rotating Houses

Go to the link: http://www.mathsnet.net/geometry/solid/rotatinghouses.html

http://www.mathsnet.net/geometry/solid/rotatinghouses.html

72

Task 2:

Find the surface area & volume of the following figures.

Solids Volume Surface Area

73

Task 3:

Frame questions involving the application of surface area and volumes based on the

pictures given below:

Pictures Write question based on the picture

74

Task 4: Do the following

1. Part of an iron pillar is in the form of a right circular cylinder and remaining is in the

form of a right circular cone. The radius of the base of the cone and the cylinder is 8

cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the

weight of the pillar, if 1 cm3 of iron weighs 7.8 gm.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

2. A company manufactures toys of the following

shape. The height of left conical part is 7 cm and

radius is 3.5 cm. The radius of the cylindrical part is 7

cm and the height is 2 cm. The total height of the toy

75

is 12.5 cm. How much paint is required to paint 225 such toys?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

3. Three identical double napped cones are placed one above the

other to form a decorative piece, which stands on a cylindrical

base. The total height is 25 inch and the height of cylinder is 4

inch. The radius of the cones is 3.5 inch and that of the cylinder is

6 inch. What is the total volume of the piece?

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

_____________________________________________________________________________

4. Writing Maths

Explain, how will you find the amount of polish required to polish the vessels below all

over.

76

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

77

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

78


Parameter


area of solids made up of

combination of two or

more solids.

Able to find the volume

of solids made up of

combination of two or

more solids.

79



Converssion of Solids

Name of Student _________________ Date_____________

Task 1: Take 200 gm of clay. Make a cylinder from this clay (use all clay). Note down

the dimension of your cylinder.

Now, make a cone from the cylinder using all the clay. Note the dimension of the cone.

Again change the cone to a sphere using all the clay. Note the radius of the sphere.

Change the sphere into a cube and then to a cuboid using the clay completely. Note

their dimensions also.

Rajan claimed that the surface area of all these will be same. Reflect.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Ritu claimed that their volume will be same. Reflect.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Task 2: Based on the solids made above, complete the table given below:

Solids made Dimensions Volume Surface area

Cylinder

80

Cone

Sphere

Cube

Cuboid

81

When one solid is converted into another, its volume is conserved but surface area may change.

Reflect.

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

_____________________________________________________________________________

Task 3: Do the following questions:

1. Three metal cubes with edges 3 cm, 4 cm and 5 cm are melted to form a single cube.

Find the edge of this new cube.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

82

2. A measuring jar of internal diameter 10 cm is partially filled with water. Four equal

spherical balls, each of diameter 2 cm, are dropped in it. The balls sink to the bottom

of the jar. What will be the change in the level of the water in the jar?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

3. A river 2 m deep and 45 m wide is flowing at the rate of 3 km per hour. Find the

amount of water that runs into the sea per minute.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

83

4. How many cubes of side ½ cm are required to build a cube of volume 8 cu.cm.?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

5. A concrete truck arrives at a job site holding 7.8 m3 of concrete. If the platform being

constructed is 5 m across and 2 m thick, how long will the platform be if constructed

from the amount of concrete on the truck?

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

6. A conical vessel whose internal radius is 5cm and height 24cm is full of water. The

water is emptied into a cylindrical vessel with internal radius 10cm. Find the height

to which the water rises in the cylindrical vessel.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

84

___________________________________________________________________________

__________________________________________________________________________

7. The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of

28 mm diameter. Find the length of the wire.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

8. A solid metallic cylinder of radius 14cm and height 21cm is melted and recast into 72

equal small spheres. Find the radius of one such sphere.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

__________________________________________________________________________

85


Parameter


area of solid obtained

when one solid is

converted into another

form by recasting

Able to find volume of

the solid obtained when

one solid is converted

into another form by

recasting

86


Post Content (PCW1)


1. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The

diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm.

Find the inner surface area of the vessel.

2. A conical vessel with internal radius 6 cm and height 8 cm is completely filled with

water. A sphere is lowered into the water and its size is such that when it touches

the sides, it is just immersed. Find the volume of water overflows.

3. A given amount of wax in cylindrical form is heated in a metal container and then

poured into another container. A new candle is formed which is shaped like a fish.

Fill in the blanks

(a) The volume of the wax _______________ (is changed/remains same)

(b) The total surface Area ________________ (is changed/remains same)

4. How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be

melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm?

5. A wooden ariticle was made by scooping out a hemisphere from each end of a

solid cylinder. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm,

find the total surface area of the article.

6. A sphere of radius 3 cm is dropped into a cylindrical vessel partly filled with

water. The radius of the vessel is 6 cm. If the sphere is submerged completely, by

how much will the surface of water be raised?

7. The radii of the ends of the frustum of a cone are 14 cm and 21 cm and the slant

height is 8 cm. Find the area of the curved surface.

87

8. Find the volume of a frustum of a cone whose face radii are 7 m and 4m and height

is 4m.

9. A lamp shade made of a special chart paper is in the form of a frustum of a cone

open at both ends. The radii of its ends are 16 cm and 24 cm and its height is 6 cm.

Find the cost of paper used if one square m costs Rs 0.70.

10. A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform

thickness. If the external radius of the base of the cylinder is 5 cm and its height is

32 cm, find the uniform thickness of the cylinder.

88


Post Content (PCW2)


Multiple Choice Questions

1. The total surface area of a solid hemisphere of radius r is

(A) r2 (B) 2 r2 (C) 3 r2 (D) 4 r2

2. The volume and the surface area of a sphere are numerically equal, then the radius

of sphere is

(A) 0 units (B) 1 units (C) 2 units (D) 3 units

3. A cylinder, a cone and a hemisphere are of the same base and of the same height.

The ratio of their volumes is

(A) 1 : 2 : 3 (B) 2 : 1 : 3 (C) 3 : 1 : 2 (D) 3 : 2 : 1

4. Small spheres, each of radius 2cm, are made by melting a solid iron ball of radius 6

cm, then the total number of small spheres is

(A) 9 (B) 6 (C) 27 (D) 81

5. A solid sphere of radius r cm is melted and recast into the shape of a solid cone of

height r. Then the radius of the base of cone is

(A) 2r (B) r (C) 4r (D) 3r

6. Three solid spheres of diameters 6 cm, 8 cm and 10 cm are melted to form a single

solid sphere. The diameter of the new sphere is

(A) 6 cm (B) 4.5 cm (C) 3 cm (D) 12 cm

7. The radii of the ends of a frustum of a cone 40 cm high are 38 cm and 8 cm. The

slant height of the frustum of cone is

(A) 50 cm (B) 10√7 cm (C) 60.96 cm (D) 4√2 cm.

8. A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface

area after such cutting?

(A) 4% (B) 300% (C) 75% (D) 400%

89

9. If we reduce the height of a cylinder by ¼ and double the radius, which of the

following will hold true?

A. Volume of the cylinder will double

B. Volume of the cylinder will remain unchanged

C. Volume of the cylinder will reduce to ½

D. None of the above

10. If we reduce the height of a cylinder by ¼ and double the radius, which of the

following will hold true?

A. Lateral Surface Area of the cylinder will double

B. Lateral Surface Area of the cylinder will remain unchanged

C. Lateral Surface Area of the cylinder will reduce to ½

D. None of the above

90


Post Content (PCW3)


Design and build a model of a house

Work in groups to make a model of a house.

Hints and Suggestions:

The scale should be 1 inch = 4 feet

Material to be used: Paper, wood, etc.

The model should not exceed beyond ½ sq. mt.

All three dimensional solid objects should be used. Namely Cube, Cuboid, Cylinder, Sphere, hemi-sphere, cone and frustum.

Students are expected to find innovative ways to use the objects in innovative/creative ways.

(Fig. 1)

Expectations from the project report:

1. Architectural layout of the model house

2. A picture of the model prepared

3. Cost of painting the model house externally

4. Volume of material used in building the model house

91

Student’s Worksheet 13 Post Content (PCW4)


Refresh Your Memory

Solid Draw

Figure

Write

Dimensions

Formula of

Volume

Formula of

LSA/CSA

Formula of

TSA

Cube

Cuboid

Cylinder

Hollow

Cylinder

Cone

Sphere

Hemisphere

Hemispherical

bowl of certain

thickness

92

Suggested Videos & Extra Readings














http://www.youtube.com/watch?v=glr5OhksSmw&feature=relmfu

http://www.youtube.com/watch?v=SdgV94_HfxI&feature=related

http://www.youtube.com/watch?v=aefdZW3htIw&feature=related

http://www.youtube.com/watch?v=yioM-LCyh0k&NR=1




http://www.beaconlearningcenter.com/weblessons/solidpatterns/default.htm#page1















http://www.youtube.com/watch?v=glr5OhksSmw&feature=relmfu

http://www.youtube.com/watch?v=SdgV94_HfxI&feature=related

http://www.youtube.com/watch?v=aefdZW3htIw&feature=related

http://www.youtube.com/watch?v=yioM-LCyh0k&NR=1




http://www.beaconlearningcenter.com/weblessons/solidpatterns/default.htm#page1


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CENTRAL BOARD OF SECONDARY EDUCATION

CBSE-i X Mathematics - NIMS Dubai – N.I. Model School ... CLASS X (Core) Mathematics Surface Area...

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Transcript of CBSE-i X Mathematics - NIMS Dubai – N.I. Model School ... CLASS X (Core) Mathematics Surface Area...