Intervention Material

8/11/2019 Intervention Material

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Republic of the Philippines

DEPARTMENT OF EDUCATION

Region IV-A CALABARZON

Division of Batangas

BAUAN NATIONAL AGRICULTURAL AND VOCATIONAL HIGH SCHOOL

San Agustin,Bauan,Batangas

INTERVENTION MATERIAL

Prepared by:

LINA C. BEJER

Math III Teacher

GABRIEL R. ROCO

Principal III


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MODULE IN MATHEMATICS

SURFACE AREA


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INTRODUCTION

Hey! Im your friend in Math. You can call me

Supermath if you want. Im just an ordinary person butthey used to call me Supermath because I have the

patience to solve it all. Cmon its easy, all you need is

patience. Just remember that patience is a virtue. Im

sure you will be good too in Math. Want to bet?


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To the Readers,

This module entitled Surface Area is careful made for you. It

tackles how to solve the surface areas of some solids step by

step to understand the lesson well.it is important that at your

age, you already competent with this lesson

I have prepared varied exercise for you to master and apply

the skills that you have learned

The Author


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OBJECTIVES

After reading this module, you should be able to:

a. To know what is surface area

b. Solve for the surface area of some solidsc. Solve problems involving surface area

d. Manifest self-confidence


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DISCUSSION

Surface Area

Surface Area is defined as the sum of the areasof the outer surfaces of a solid. These outer

surfaces are known as faces.

Having studied polygons and their areas, as well

as polyhedrons and their characteristics, it will beeasy to understand how the total area of the

surfaces of solids is obtained.


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Surface Area of a Cube

To find the surfaces area of a cube,multiply the square of the length of

side by 6.

Theorem

The surface area (SA) of a cube side (s) is given by:SA= 6s

2

SIDE

LATERAL FACE


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Example:Find the surface area of a cube with a side

of length 6cm.Solution:Using the formula for the surface area of a

cube, SA= 6s2

, we have

SA = 6s2

=6(6cm)2

= 6(36cm2)

SA = 246cm2


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Surface Area of a Rectangular Prism

To find the surface are

(SA) of a rectangular

prism, add the areas of its

faces.

Theorem

The surface area (SA) of a rectangular prism of length(I), width (W), and height (h) is given by:

SA = 2hw + 2lw + 2hl


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Example:Find the surfaces area of a rectangular

prism whose length is 7cm, width is 4 cm, and heightis 5 cm.

Solution:Using the formula for the surface area

of rectangular prism, SA = 2lw + 2hw + 2hl, we have

SA = 2lw + 2hw + 2hl

SA = 2(7cm) (4cm) + 2(5cm) (4cm) + 2(5cm)(7cm)

= 56 cm2+40 cm2+70cm2=166 cm

2


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Surface Area of a Right Square Pyramid

To find the Surface Area

of a right square pyramid,

add the area of the square

base and the areas of thefour triangular faces

Theorem

The surface area of a right square pyramid with a

base of side (s) and a slant height () is given by

SA = S2+ 4 (

) or SA = s

2+ 2 (s x )


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Example:Find the surface area of the right square

pyramid with base of side 3cm and slant height of 5cm.

Solution:Using the formula for the surface area of a

right square pyramid, SAS2

+2(S x ), we have

SA = S2+2(S x )

SA = (3cm)2+ 2[(3cm) x (5cm)]

=9cm2+2(15 cm2)=9cm

2+30cm

2

SA=39cm2


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Surface Area of a Circular Cylinder

To find the surface area of a right

circular cylinder, add the areas of

the circular bases and the area of

the rectangular region which isthe body of the cylinder.

Theorem

The surface area (SA) of a right circular

cylinder of radius (r) and height (h) is given by:

SA + or SA =


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Example:Find the surface area of a right circular

cylinder which has height and 20cm and a base

radius of 5cm.


right circular cylinder, SA = 2 , we have

SA = 2

SA =2(5 cm)(5 cm + 20 cm)SA = 2(5 cm)(25 cm)

SA = 2(125 cm2)

SA= 250 cm2


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Surface Area of a Right Circular Cone

To find the surface area of a

right circular cone, add the areas of

the base which is a circle (), and

the curved surface which is thelateral area (r).

Theorem

The surface area (SA) of a right circular cone of radius

(r) and slant height () is given by SA= + r


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Example:find the surface area of a circular cone if

the radius of its base is 3.5cm and its slant height is7.25cm.


right circular cone, SA=

+ r, we have

SA= + r

SA= (3.5 cm)2+ (3.5 cm)(7.25 cm)

SA= (12.25 cm2) + (25.375 cm2)SA= 12.25cm

2+ 25.375 cm

2

SA= 37.625cm2


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Surface Area of a Sphere

Recall that a sphere is the set of

all points in space equidistant

from a fixed point called center.

The fixed distance is called theradiusof a sphere.

Theorem

The surface area (SA) of a sphere of radius (r) is given by

SA= 4


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Example: What is the surface area of a ball with a

radius of 6cm?

Solution: Using the formula for the surface area of a

sphere, SA= 4, we have

SA = 4

SA = 4(6 cm)2

SA= 4(36 cm)2

SA= 144cm2


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Practice

SOLVING SURFACE AREAS

1. Find the surface area of a cube whose side is 4cm.

2. Find the surface area of a cylinder whose diameter of

base is 6cm and have a height of 10cm.

3. Find the surface of a rectangular prism with a length

of 6cm, a width of 3cm and a height of 2cm.

4.

A cone has a slant height of 13 cm and the radius of

the base is 6.25 cm. Find the surface area of the cone.

5. A ball has a radius of 6 cm, find its surface area.


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Exercises:1.

A cylindrical tank is 2.6 meters high. If the radius of its base is 0.92

meter, what is the surface area?

2.If a cube with a side of 2.2 cm needs a wrapper for its cover, how

many centimeters of wrapper is needed to cover the cube?

3.

Theres a cone with a radius of 5 cm and a slant height of 12 cm.

your teacher asked you to find the surface area, what will be youranswer?

4.

The third year students are constructing a square pyramid for their

project. They plan to cover it with a manila paper. If the side of the

base of the pyramid measures 2.2 meters and the height of each

triangular face is 1.6 meters. What size of manila paper will beneeded to cover the square pyramid?

5.

Jasper has a ball whose surface area is 314 cm2. He wants to know

the radius of his ball, what should be his answer?


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6.A metal tube is in the form of right circular cylinder. The radius of its

base is 4 cm and its height is 10 cm. Find the surface area of the

metal tube.7.

Find the surface area of a rectangular box with a length of 2.1 cm, a

width of 2.7 cm and a height of 3 cm.

8.A cube has a surface area of 294 cm2, what is the measure of its

side?

9.

The diameter of a spherical tank is 1.4 m. What is the surface area?10.

A refrigerator is 5.008 square meters. If its length is 0.8 meter

and its width is 0.51, what is its height?


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Keep Your Skill Sharp

Solve the following:

1.

How many square centimeters of gift wrapper is

needed to wrap a box 9cm by 15 cm by 7 cm allowing 4

cm2 for folding and pasting?

2.

Find the edge of a cube it its surface area is 384square meters?

3. Find the surface area of a square pyramid if the slant

height is 16.5 cm and a side of the base is 8 cm.

4.

Find the lateral area of a cone whose radius is 3 cmand a slant height of 5 cm.

5. What is the surface area of a marble whose diameter

is 10 millimeters?


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6. Find the surface area of a ball with a radius of 9.7

millimeters.

7.

Find the surface area of a right circular cylinder if it is

40 mm high and the radius of its base measures 10.2 mm.

8. The base edge of a square pyramid has a length of 3

dm. If each lateral face has an area of 12 dm2, what is the

total surface area of the pyramid?9. The edge of the cube measures 7.5 cm. What is the

surface area?

10.

Find the surface area of a globe, which is 6 cm in

diameter.


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Great!!! You have finished this module. Now check your answers in

Practice Solving Surface Areas, Exercises and Keeping your Skill

Sharp.Practice Solving Surface Areas

1. 96 cm2

2.

3.

4. 120.3125

5. 144

Exercises

1. 6.4768

2. 29.04

3. 266.9

4. 11.88

5. 5

6. 112

7. 40.14

8.

7 9. 1.96

10.1.6

Keeping Your Skill Sharp

1. 606 cm2

2. 8 m

3. 64 cm2

4. 24

5. 100

6. 376.36

7. 1024.08

8. 432

9. 337.5

10.36 c

Goodbye!!!

See you in the next module!


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