10-9 Surface Area

Learn to find the surface areas of prisms, pyramids, and cylinders.

10-9 Surface Area

Vocabularysurface areanet

10-9 Surface Area

The surface area of a three-dimensional figure is the sum of the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is the pattern made when the surface of a three-dimensional figure is layed out flat showing each face of the figure.

10-9 Surface AreaAdditional Example 1A: Finding the Surface Area of

a PrismFind the surface area S of the prism.Method 1: Use a net.

Draw a net to help you see each face of the prism.Use the formula A = lw to find the area of each face.

10-9 Surface AreaAdditional Example 1A Continued

A: A = 5 2 = 10B: A = 12 5 = 60C: A = 12 2 = 24D: A = 12 5 = 60E: A = 12 2 = 24F: A = 5 2 = 10

S = 10 + 60 + 24 + 60 + 24 + 10 = 188Add the areas of each face.

The surface area is 188 in2.

10-9 Surface AreaAdditional Example 1B: Finding the Surface Area of a

PrismFind the surface area S of each prism.Method 2: Use a three-dimensional drawing.

Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

10-9 Surface AreaAdditional Example 1B Continued

Front: 9 7 = 63Top: 9 5 = 45Side: 7 5 = 35

63 2 = 12645 2 = 9035 2 = 70

S = 126 + 90 + 70 = 286 Add the areas of each face.

The surface area is 286 cm2.

10-9 Surface AreaCheck It Out: Example 1A

Find the surface area S of the prism.Method 1: Use a net.

Draw a net to help you see each face of the prism.Use the formula A = lw to find the area of each face.

3 in.11 in.

6 in. 11 in.

6 in. 6 in.3 in.

3 in.

3 in.

3 in.

A

B C D EF

10-9 Surface AreaCheck It Out: Example 1A

A: A = 6 3 = 18B: A = 11 6 = 66C: A = 11 3 = 33D: A = 11 6 = 66E: A = 11 3 = 33F: A = 6 3 = 18

S = 18 + 66 + 33 + 66 + 33 + 18 = 234Add the areas of each face.

The surface area is 234 in2.

11 in.

6 in. 6 in.3 in.

3 in.

3 in.

3 in.

A

B C D EF

10-9 Surface AreaCheck It Out: Example 1B

Find the surface area S of each prism.Method 2: Use a three-dimensional drawing.

Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

6 cm 10 cm8 cm

topfront side

10-9 Surface AreaCheck It Out: Example 1B Continued

Side: 10 8 = 80Top: 10 6 = 60Front: 8 6 = 48

80 2 = 16060 2 = 12048 2 = 96

S = 160 + 120 + 96 = 376 Add the areas of each face.The surface area is 376 cm2.

6 cm 10 cm8 cm

topfront side

10-9 Surface Area

The surface area of a pyramid equals the sum of the area of the base and the areas of the triangular faces. To find the surface area of a pyramid, think of its net.

10-9 Surface AreaAdditional Example 2: Finding the Surface Area of a

PyramidFind the surface area S of the pyramid.

S = area of square + 4 (area of triangular face)

S = 49 + 4 28S = 49 + 112

Substitute.

S = s2 + 4 ( bh) 12__

S = 72 + 4 ( 7 8)12__

S = 161The surface area is 161 ft2.

10-9 Surface AreaCheck It Out: Example 2

Find the surface area S of the pyramid.

S = area of square + 4 (area of triangular face)

S = 25 + 4 25S = 25 + 100

Substitute.

S = s2 + 4 ( bh) 12__

S = 52 + 4 ( 5 10)12__

S = 125The surface area is 125 ft2.

5 ft

5 ft

10 ft

10 ft5 ft

10-9 Surface Area

The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface.

To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base.

Helpful Hint

10-9 Surface AreaAdditional Example 3: Finding the Surface Area of a

CylinderFind the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S = area of curved surface + 2 (area of each base)Substitute.S = h (2r) + 2 (r2)

S = 7 (2 4) + 2 ( 42)

ft

10-9 Surface AreaAdditional Example 3 Continued

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S 7 8(3.14) + 2 16(3.14)S 7 25.12 + 2 50.24

The surface area is about 276.32 ft2.

Use 3.14 for .

S 175.84 + 100.48S 276.32

S = 7 8 + 2 16

10-9 Surface AreaCheck It Out: Example 3

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S = area of curved surface + 2 (area of each base)Substitute.S = h (2r) + 2 (r2)

S = 9 (2 6) + 2 ( 62)

6 ft

9 ft

10-9 Surface AreaCheck It Out: Example 3 Continued

Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.

S 9 12(3.14) + 2 36(3.14)S 9 37.68 + 2 113.04

The surface area is about 565.2 ft2.

Use 3.14 for .

S 339.12 + 226.08S 565.2

S = 9 12 + 2 36

10-9 Surface Area

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

10-9 Surface AreaLesson Quiz

Find the surface area of each figure. Use 3.14 for .

1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft

2. cylinder with radius 3 ft and height 7 ft

3. Find the surface area of the figure shown.

214 ft2

188.4 ft2

208 ft2

10-9 Surface Area

1. Find the surface area of a rectangular prism with base length 7 ft, width 6 feet, and height 9 ft.

A. 318 ft2

B. 306 ft2

C. 300 ft2

D. 298 ft2

Lesson Quiz for Student Response Systems

10-9 Surface Area

2. Find the surface area of a cylinder with radius 5 ft and height 8 ft. Use 3.14 for .

A. 576.8 ft2

B. 408.2 ft2

C. 376.2 ft2

D. 251.2 ft2

Lesson Quiz for Student Response Systems

10-9 Surface Area

3. Find the surface area of the figure shown.

A. 162 ft2

B. 152 ft2

C. 142 ft2

D. 132 ft2

Lesson Quiz for Student Response Systems