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
