1 ch10 l7
TRANSCRIPT
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10-7 Surface Area
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
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Warm UpIdentify the figure described.
1. two parallel congruent faces, with the other faces being parallelograms
2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles
prism
pyramid
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Problem of the Day
Which figure has the longer side and by how much, a square with an area of 81 ft2 or a square with perimeter of 84 ft?
A square with a perimeter of 84 ft; by 12 ft
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Learn to find the surface areas of prisms, pyramids, and cylinders.
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Vocabulary
surface areanet
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The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net. A net is the pattern made when the surface of a solid figure is layed out flat showing each face of the figure.
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Additional Example 1A: Finding the Surface Area of a Prism
Find the surface area S of the prism.
A. 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.
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Additional Example 1A Continued
A: A = 5 2 = 10
B: A = 12 5 = 60
C: A = 12 2 = 24
D: A = 12 5 = 60
E: A = 12 2 = 24
F: A = 5 2 = 10
S = 10 + 60 + 24 + 60 + 24 + 10 = 188Add the areas of each face.
The surface area is 188 in2.
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Additional Example 1B: Finding the Surface Area of a Prism
Find the surface area S of each prism.
B. 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.
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Additional Example 1B Continued
Front: 9 7 = 63
Top: 9 5 = 45
Side: 7 5 = 35
63 2 = 126
45 2 = 90
35 2 = 70
S = 126 + 90 + 70 = 286 Add the areas of each face.
The surface area is 286 cm2.
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Try This: Example 1A
Find the surface area S of the prism.
A. 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 E
F
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Try This: Example 1A
A: A = 6 3 = 18
B: A = 11 6 = 66
C: A = 11 3 = 33
D: A = 11 6 = 66
E: A = 11 3 = 33
F: A = 6 3 = 18
S = 18 + 66 + 33 + 66 + 33 + 18 = 234
Add 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 E
F
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Try This: Example 1B
Find the surface area S of each prism.
B. 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 cm
8 cm
topfront side
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Try This: Example 1B Continued
Front: 10 8 = 80
Top: 10 6 = 60
Side: 8 6 = 48
80 2 = 160
60 2 = 120
48 2 = 96
S = 160 + 120 + 96 = 376 Add the areas of each face.
The surface area is 376 cm2.
6 cm 10 cm
8 cm
topfront side
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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.
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Additional Example 2: Finding the Surface Area of a Pyramid
Find the surface area S of the pyramid.S = area of square + 4 (area of
triangular face)
S = 49 + 4 28
S = 49 + 112
Substitute.
S = s2 + 4 ( bh) 12__
S = 72 + 4 ( 7 8)12__
S = 161The surface area is 161 ft2.
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Try This: Example 2
Find the surface area S of the pyramid.
S = area of square + 4 (area of triangular face)
S = 25 + 4 25
S = 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 ft
5 ft
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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
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Additional Example 3: Finding the Surface Area of a Cylinder
Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.
S = area of lateral surface + 2 (area of each base)
Substitute.S = h (2r) + 2 (r2)
S = 7 (2 4) + 2 ( 42)
ft
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Additional 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 + 100.48
S 276.32
S = 7 8 + 2 16
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Try This: Example 3
Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth.
S = area of lateral surface + 2 (area of each base)
Substitute.S = h (2r) + 2 (r2)
S = 9 (2 6) + 2 ( 62)
6 ft
9 ft
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Try This: 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 + 226.08
S 565.2
S = 9 12 + 2 36
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Lesson 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.
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214 ft2
188.4 ft2
208 ft2