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Learn to find the surface area of prisms and

cylinders.

Vocabulary

surface area lateral face lateral surface

Surface area is the sum of the areas of all

surfaces of a figure. The lateral faces of a

prism are parallelograms that connect the bases.

The lateral surface of a cylinder is the curved

surface.

(No Transcript)

Additional Example 1 Finding Surface Area

Find the surface area of each figure

A. S 2pr2 2prh

2p(42) 2p(4)(6)

80p in2 ? 251.2 in2

B. S 2B Ph

204 ft2

Try This Example 1

Find the surface area of each figure

15 cm

A. S 2pr2 2prh

3 cm

2p(152) 2p(15)(3)

540p in2 ? 1695.6 cm2

7 cm

7 cm

6 cm

B. S 2B Ph

10 cm

7 cm

252 cm2

Additional Example 2 Exploring the Effects of

Changing Dimensions

A cylinder has diameter 8 in. and height 3 in.

Explain whether tripling the height would have

the same effect on the surface area as tripling

the radius.

They would not have the same effect. Tripling the

radius would increase the surface area more than

tripling the height.

Try This Example 2

A cylinder has diameter 6 in. and height 2 in.

Explain whether doubling the height would have

the same effect on the surface area as doubling

the radius.

S 2pr2 2pr(2h)

S 2pr2 2p(2r)h

S 2pr² 2prh

2p(3)2 2p(3)(4)

2p(6) 2 2p(3)(2)

2p(3)2 2p(3)(2)

42p in2 131.88 in2

84p in2 263.76 in2

30p in2 94.2 in2

They would not have the same effect. Doubling the

radius would increase the surface area more than

doubling the height.

Additional Example 3 Application

A cylindrical soup can is 7.6 cm in diameter and

11.2 cm tall. What is the area of the label that

covers the side of the can?

Only the lateral surface needs to be covered.

L 2?rh

2?(3.8)(11.2)

The diameter is 7.6 cm, so r 3.8 cm.

267.3 cm2

Try This Example 3

A cylindrical storage tank that is 6 ft in

diameter and 12 ft tall needs to be painted. The

paint will cover 100 square feet per gallon. How

many gallons will it take to paint the tank?

S 2?r2 2?rh

The diameter is 6 ft, so r 3 ft.

2?(32) 2?(3)(12)

282.6 ft2

Move the decimal point 2 places to the left to

divide by 100.

2.826 gal

Lesson Quiz

Find the surface area of each figure to the

nearest tenth. Use 3.14 for p. 1. the triangular

prism 2. the cylinder

360 cm2

320.3 in2

3. All outer surfaces of a box are covered with

gold foil, except the bottom. The box measures 6

in. long, 4 in. wide, and 3 in. high. How much

gold foil was used?

84 in2

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