GEOMETRYHELP

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

Draw a net for the cube.

Find the area of one face. 112 = 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.

Quick Check

Surface Areas of Prisms and CylindersLESSON 11-2

Additional Examples

GEOMETRYHELP

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. + 2B to find the surface area of the prism. The area B of the base is ap, where a is the apothem and p is the perimeter.1

2

Draw the base.

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

The triangle has sides of length 18 cm, so p = 3 • 18 cm, or 54 cm.

Surface Areas of Prisms and CylindersLESSON 11-2

Additional Examples

GEOMETRYHELP

The area of each base of the prism is 81 3 cm2.

(continued)

S.A. = L.A. + 2B Use the formula for surface area.

= ph + 2B

Rounded to the nearest whole number, the surface area is 821 cm2.

81 3B = ap =12

12 3 3 54 =

9 3 3

3 3

9 3

a = = = 3 3 Rationalize the denominator.

Surface Areas of Prisms and CylindersLESSON 11-2

Additional Examples

Quick Check

= 540 + 162 3

Use a calculator.

9 = 3 a longer leg 3 shorter leg

2(81 3 ) Substitute = (54)(10) +

GEOMETRYHELP

S.A. = L.A. + 2B Use the formula for surface area of a cylinder.

= 2 (6)(9) + 2 (62) Substitute 6 for r and 9 for h.

The surface area of the cylinder is 180 ft2.

Quick Check

= 2 rh + Substitute the formula for lateral area of a cylinder and area of a circle.

2( r 2)

= 108 + Simplify.

= 180

72

Surface Areas of Prisms and CylindersLESSON 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 .

GEOMETRYHELP

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 = .d2

S.A. = L.A. + 2B S.A. = L.A. + 2B

Cornmeal Container Barley Container

Use the formula for surface area of a

cylinder.

= 2 rh + 2 r 2 = 2 rh + 2 r 2Substitute the formulas for lateral area of a

cylinder and area of a circle.

Surface Areas of Prisms and CylindersLESSON 11-2

Additional Examples

GEOMETRYHELP

Cornmeal Container Barley Container

= 32 = 42

Because 42 in.2 32 in.2, the barley container has the greater surface area.

(continued)

= (2)(6) + (22 ) = (3)(4) + (32 )Substitutefor r and h.

2 2 2 2

= 24 + = 24 + Simplify.8 18

Surface Areas of Prisms and CylindersLESSON 11-2

Additional Examples

Quick Check