Maths Project 9 Class

8/3/2019 Maths Project 9 Class

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Introduction

This presentation is on the topic Volume and

Surface Areas.

This is presented before to prove how volume

of cubes,

cuboids and surface areas of a triangle is

verified by

practical method with the help of a Rubikscube. Also it

is presented to give a brief description of a

Rubiks cube. Hope

That the reader finds interest and

Learns the verifications.

Thank you..


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Rubiks Cube

Rubiks cube is a 3-d mechanical puzzle game invented in 1974 by

Hungarian sculptor and professor of architecture Erno` Rubik.

In a

classic Rubik's Cube, each of the six faces is covered by nine

stickers,

each of one of six solid colours, (traditionally white, red, blue,orange,

green, and yellow). A pivot mechanism enables each face to turn

independently, thus mixing up the colours. For the puzzle to be

solved,

each face must be returned to consisting of one colour. Similarpuzzles

have now been produced with various numbers of shapes, like

pyramid

etc. An ordinary classic Rubiks cube looks like this:


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Verification of Volume of Cube

by Practical Means

As you can see, there are three layers of cuboids

in a single cube.

So to find the volume of whole cube, we have to

find the volume of every layer of cuboid. Let us

take one coloured square as one unit.

Now, for thevolume of 1st cuboid:

V=l X b X h

=3units X 3units X 1 unit

=9 units


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Similarly, for next 2 cuboids also, the answer will

come 9 units.

To find the volume of whole cube we have to add

the volume of all 3 cuboids.

The answer will come 9+9+9=27 units3

By using the formula also the answer will be:

V=a3

=33

=27 units.

Hence we observe that, by practical method too,

we can find the volume of a cube.


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Verification of Volume of

Cuboid by Practical Method

If we cover one of the layers of cuboid we will

find that there are 2 layers forming a cuboid.

Now,again the volume of 1 layer of cuboid is

measured:

V=l X b X h

=3 X 3 X 1

=9units3

For the second layer also, the volume is to be

measured which is equal to the volume of 1st


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cuboid i.e. 9units.On, adding volume of both the

cuboids we will get the volume of whole cuboid i.e.

Total volume =volume of 1st cuboid + volume of 2nd

cuboid

= 9 units +9 units=18units3

According to the formula also, volume of whole

cuboid=l X b X h

=3 X 3 X 2

=18 units.

Hence, we observe that the volume of the cuboid

can also be verified by practical method.


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Verification of

Surface Area of Trianlge

If we cover the cube diagonally then its half

portion is covered. Therefore, we see that it is

forming a circle.

If we count the total number of units, then we

shall get the surface area of the triangle. On

counting the number of units we get,

Area=1/2+1/2+1/2+1+1+1

=41/2 units2.


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According to the formula, the surface area of the

triangle will be:

Area=1/2 X b X h

=1/2 X 3 X 3

=1/2 X 9

=41/2 units2

Hence, we observe that the surface area of

triangle can also be verified by practical method.


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Conclusion

Thus at the end of my presentation, I

therefore conclude that the volumes of cubes

and cuboids and the area of triangle can be

verified by practical methods. Like this

the areas of many other polygons such as

square, rectangle, parallelograms,

trapezium, rhombus and even hexagon. I once

again thank my teacher, Dinesh

Pandey sir. And also I would like to thank all

those unknown writer who helped

me by writing those books which helped me

prepare my presentation.

Thank You..


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Acknowledgement Through this acknowledgment, we express

our sincere gratitude to all those

people who have been associated with this

assignment and have helped us with it

and made it a worthwhile experience.

Firstly we extend our thanks to the various

people who have shared their opinions

and experiences through which we received

the required information crucial for our

report.

Finally, we express our thanks to our teacher

Dinesh Pandey sirwho gave us

this opportunity to learn the subject in a

practical approach, who guided us


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and gave us valuable suggestions regarding

the project report.

Submitted By:-

Hrashit Lohani

Thank You

Index

S.no. Name of the

Topic

Page number

1 Introductio

n

1

2 Rubiks

Cube

2

3 Verification

of volume

of cube

3

4 Verification 5


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of volume

of cube

5 Verification

of area of

triangle

7

6 Conclusion 9


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Maths Project 9 Class

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