CONFIDENTIAL 1

Algebra 1Algebra 1

Surface area of Surface area of solid Figures solid Figures

CONFIDENTIAL 2

1) Calculate the volume of the Triangular prism with altitude = 7.6 cm , base = 11 cm and the

height is = 15 cm. 627 cm3

2) The given cylinder has radius = 13 cm and the height = 16 cm. A cone of radius = 9 cm and

height = 13 cm is cut from the cylinder. What is the volume of the remaining piece? 7388.42 cm3

3) If the volumes of two cubes are in the ratio 64 : 1, then what is the ratio of their edges? 4:1

4) The radius of a cylinder is decreased to 1/5th of the original radius. How many times will its height increase, if its volume remains the same? 25 times

Warm UpWarm Up

CONFIDENTIAL 3

Surface area

The surface area of a solid figure is the sum of the areas of all faces of the figure.

The surface area of a rectangular solid is expressed in square units.

An area of study closely related to solid geometry is nets of a solid. Imagine making cuts along

some edges of a solid and opening it up to form a plane figure. The plane figure is called the net of

the solid.

CONFIDENTIAL 4

In general,

Surface Area of solid figures= 2 x area of the base +perimeter of the base x height

If,

B = area of the base

P = perimeter of the base

h = height

SA = Surface Area

Then,SA = 2B +Ph

CONFIDENTIAL 5

Cubes

A cube is a three-dimensional figure with all edges of the same length.

If s is the length of one of its sides, then SA = 2(s2) + (4s)s = 6s2

s

sss s

s

s s

s

CONFIDENTIAL 6

Calculate the surface area of the cube with length of sides = 7 cm.

Volume of the cube = 6s2

= 6 x (7)2

= 6 x 49 = 294

Surface Area of the cube = 294 cm2

7 7

7

CONFIDENTIAL 7

Triangular prism

b

a

b

h

c d

SA = 2( 1 ) + (b + c + d)h 2ab

SA = ab + (b + c + d)h

a

b

h

c

d

CONFIDENTIAL 8

Calculate the surface area of the regular triangular prism.

Surface area of the triangular prism = a x b + (b + c + d)h = 5 x 8 + (8 + 8 + 8) x 10 = 40 + 240= 280

Surface area of the cuboid = 280 cm2

5

8

10

CONFIDENTIAL 9

Now you try!

2) Calculate the surface area of the given triangular prism. 645 units2

1) The surface area of a cube is 294 ft2. Find the length of each edge. 7ft

5

8

11

6

78

CONFIDENTIAL 10

Rectangular prism

l w

h

l w

h

SA = 2B + Ph

SA = 2(lw) + (2l + 2w)h

CONFIDENTIAL 11

8 4

7

Calculate the surface area of the given rectangular prism.

Surface area of the rectangular prism = 2(lw) + (2l + 2w)h = 2(8 x 4) + (2 x 8 + 2 x 4) x 7 = 2 x 32 + (16 + 8) x 7 = 64 + 168 = 232

Surface area of the rectangular prism = 268 cm2

CONFIDENTIAL 12

Regular square prism

s s

h

SA = 2B + Ph

SA = 2(s2) + (4s)h

s

h

CONFIDENTIAL 13

Calculate the surface area of the given Regular square prism.

Surface area of the Regular square prism = 2(s2) + (4s)h = 2(8 x 8) + (4 x 8) x 11 = 2 x 64 + 32 x 11 = 128 + 352 = 480

Surface area of the regular square prism = 480 cm2

8 8

11

CONFIDENTIAL 14

Regular pentagonal prism

s

h

a

SA = 2(1ans) + nsh 2

SA = 2(1a)(5)s + 5sh 2

SA = 5as + 5sh

sa

h

CONFIDENTIAL 15

8

9

6

Calculate the surface area of the given Regular pentagonal prism.

Surface area of the Regular square prism = 5as + 5sh = 2 x 6 x 8 + 5 x 8 x 9 = 2 x 48 + 5 x 72 = 96 + 360 = 456

Surface area of the regular square prism = 456 cm2

CONFIDENTIAL 16

Now you try!

2) Calculate the surface area of the given Regular pentagonal prism. 180 sq units

1) The surface area of a regular square prism is 294 ft2 and height 10 ft. Find the length of

each edge of the base. 5.7ft

4

6

3

CONFIDENTIAL 17

SA = 1as + 3sl 2 2

SA = B + n(1sl) 2

SA = 1as + (3)(1sl) 2 2

l = slant height

l

a

s

l

a

s

Regular triangular pyramid

CONFIDENTIAL 18

5

4

6

Calculate the surface area of the given Regular triangular pyramid.

Surface area of the Regular triangular pyramid= 1as + 3sl 2 2= 1 x 4 x 6 + 3 x 6 x 5 2 2= 18 + 45 = 63

Surface area of the regular triangular pyramid = 63 cm2

CONFIDENTIAL 19

l

s

SA = B + n(1sl) 2

SA = s2 + (4)(1sl) 2

SA = s2 + 2sl

Regular square pyramid

s s

hl

CONFIDENTIAL 20

Calculate the surface area of the given Regular square pyramid.

Surface area of the Regular square pyramid= s2 + 2sl

=8 x 8 + 2 x 8 x 7= 64 + 112 = 176

Surface area of the regular square pyramid = 176 cm2

8 8

h7

CONFIDENTIAL 21

Now you try!

2) Calculate the surface area of the given Regular square pyramid. 280 sq units

10 10

h9

5

8

9

1) Calculate the surface area of the given Regular triangular pyramid. 103.5 sq units

CONFIDENTIAL 22

Cylinder

h

r

P

SA = 2B + Ph

SA = 2(Π r2) + (2 Π r)h

r

h

CONFIDENTIAL 23

Calculate the surface area of the given cylinder.

Surface area of the cylinder= 2(Π r2) + (2 Π r)h

=2 x (3.14 x 5 x 5 ) + (2 x 3.14 x 5 ) x 8= 157 + 251.2 = 408.2

Surface area of the cylinder = 408.2 cm2

5

8

CONFIDENTIAL 24

SA = 4 Π r2

Sphere

r

CONFIDENTIAL 25

Calculate the surface area of the given sphere.

Surface area of the sphere= 4 Π r2

=4 x 3.14 x 10 x 10 = 1256

Surface area of the sphere = 1256 cm2

10

CONFIDENTIAL 26

Now you try!

2) Calculate the surface area of the given sphere. 804.6 sq units

1) Calculate the surface area of the given cylinder. 748 sq units

8

7

10

CONFIDENTIAL 27

Assessment

1) What is the perimeter of the floor, if the area of the four walls is equal to 2700 ft2 and its height is 12 ft?

225 ft

2) The perimeter of one face of a cube is 48 cm. What is its surface area? 864 sq cm

CONFIDENTIAL 28

3) The base radius of a cylinder is 2 cm and its height is 5 cm. What is the resultant surface area of the cylinder, if the radius is increased by 2 times?

326.86 sq cm

4) Calculate the surface area of the given Regular triangular pyramid. 139.5 sq units

8

7

9

CONFIDENTIAL 29

5) Calculate the surface area of the given Regular pentagonal prism. 225 sq units

4.5

7

3

6) Calculate the surface area of the given Regular square pyramid. 133 sq units

7 7

h6

CONFIDENTIAL 30

7) Calculate the surface area of the sphere with radius = 34 cm. 14519.36 sq cm

8) The base area of a square pyramid is 49 in2. What is the surface area of the pyramid , if the slant height of the pyramid is 12 in? 217 sq in

CONFIDENTIAL 31

9) A rectangular tin sheet of 44 in. long and 20 in. broad is rolled along its length to form a cylinder by making the opposite edges just touch each other. What is the base radius of the cylinder formed?

5.49 in

10) What is the lateral area of a cube, if the area of each face of the cube is 16 ft2? 64 sq ft

CONFIDENTIAL 32

11) The figure shows a rectangular prism with a cylinder which has been removed from it. What is

the total surface area of the given solid? Round the answer to the nearest ten. 530 sq units

107

103

5

CONFIDENTIAL 33

In general,

Surface Area of solid figures= 2 x area of the base +perimeter of the base x height

If,

B = area of the base

P = perimeter of the base

h = height

SA = Surface Area

Then,SA = 2B +Ph

Let’s review

CONFIDENTIAL 34

Cubes

A cube is a three-dimensional figure with all edges of the same length.

If s is the length of one of its sides, then SA = 2(s2) + (4s)s = 6s2

s

sss s

s

s s

s

review

CONFIDENTIAL 35

Triangular prism

b

a

b

h

c d

SA = 2( 1 ) + (b + c + d)h 2ab

SA = ab + (b + c + d)h

a

b

h

c

d

review

CONFIDENTIAL 36

Rectangular prism

l w

h

l w

h

SA = 2B + Ph

SA = 2(lw) + (2l + 2w)h

review

CONFIDENTIAL 37

Regular pentagonal prism

s

h

a

SA = 2(1ans) + nsh 2

SA = 2(1a)(5)s + 5sh 2

SA = 5as + 5sh

sa

h

review

CONFIDENTIAL 38

SA = 1as + 3sl 2 2

SA = B + n(1sl) 2

SA = 1as + (3)(1sl) 2 2

l = slant height

l

a

s

l

a

s

Regular triangular pyramid

review

CONFIDENTIAL 39

l

s

SA = B + n(1sl) 2

SA = s2 + (4)(1sl) 2

SA = s2 + 2sl

Regular square pyramid

s s

hl

review

CONFIDENTIAL 40

Cylinder

h

r

P

SA = 2B + Ph

SA = 2(Π r2) + (2 Π r)h

r

h

review

CONFIDENTIAL 41

SA = 4 Π r2

Sphere

r

review

CONFIDENTIAL 42

You did a great job You did a great job today!today!