Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples

Use a net to find the surface area of the cube.

Draw a net for the cube.

Find the area of one face. 11 2 = 121 The area of each face is 121 in.

2 .

Surface Area = sum of areas of lateral faces + area of bases = (121 + 121 + 121 + 121) + (121 + 121) = 6 • 121 = 726 Because there are six identical faces, the surface area is 726 in.

2 .

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Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples

Find the surface area of a 10-cm high right prism with triangular bases having 18-cm edges. Round to the nearest whole number.

Use the formula L.A. =

ph

to find the lateral area and the formula S.A. = L.A. + 2

B

base is 2

ap

to find the surface area of the prism. The area , where

a

is the apothem and

p

is the perimeter.

B

of the The triangle has sides of length 18 cm, so

p

= 3 • 18 cm, or 54 cm.

Draw the base.

Use 30 °-60°-90° triangles to find the apothem.

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Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples Quick Check (continued)

9 = 3 

a

longer leg  3  shorter leg

a

= 9 3  3 3

=

9 3 3

=

3 3 Rationalize the denominator.

B

= 1 2

a p

= 1 2  3 3  54 = 81 3 The area of each base of the prism is 81 3 cm 2 .

S.A. = = L.A.

ph

+ 2 + 2

B B

Use the formula for surface area.

= ( 54 )( 10 ) + 2( 81 3 ) Substitute = 540 + 162 3 Use a calculator.

Rounded to the nearest whole number, the surface area is 821 cm 2 .

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Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples

The radius of the base of a cylinder is 6 ft, and its height is 9 ft. Find its surface area in terms of .

S.A. = L.A.

+ 2

B

Use the formula for surface area of a cylinder.

= 2

rh

Substitute the formula for lateral area of a cylinder and area of a circle.

= 2 (6)(9) + 2 (6 2 ) Substitute 6 for

r

and 9 for

h

.

Simplify.

= 180 The surface area of the cylinder is 180 ft 2 .

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Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples

A company sells cornmeal and barley in cylindrical containers. The diameter of the base of the 6-in. high cornmeal container is 4 in. The diameter of the base of the 4-in. high barley container is 6 in. Which container has the greater surface area?

Find the surface area of each container. Remember that

r d

= .

2

Cornmeal Container

S.A. = L.A.

+ 2

B

Use the formula for surface area of a cylinder.

Barley Container

S.A. = L.A.

+ 2

B

= 2

rh

+ 2

r

2 Substitute the formulas for lateral area of a cylinder and area of a circle.

= 2

rh

+ 2

r

2

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Surface Areas of Prisms and Cylinders LESSON 11-2 Additional Examples (continued)

Cornmeal Container Barley Container

= 2 (2)(6) + 2 (2 2 ) Substitute for

r

and

h

.

= 2 = 24 + 8 = 32 Simplify.

= 42 Because 42 in.

2 surface area.

 32 in.

2 , the barley container has the greater (3 2 )

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