Holt CA Course 1

10-10 Surface Area

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Holt CA Course 1

10-10 Surface Area

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

Holt CA Course 1

10-10 Surface Area

AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = d–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).Also covered: AF3.2

California Standards

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Holt CA Course 1

10-10 Surface Area

Vocabulary

surface areanet

Holt CA Course 1

10-10 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 an arrangement of two-dimensional figures that can be folded to form a three-dimensional figure.

Holt CA Course 1

10-10 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

Holt CA Course 1

10-10 Surface AreaAdditional Example 1: 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.

Holt CA Course 1

10-10 Surface AreaAdditional 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.

Holt CA Course 1

10-10 Surface AreaAdditional Example 1: 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.

Holt CA Course 1

10-10 Surface AreaAdditional 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.

Holt CA Course 1

10-10 Surface AreaAdditional 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 = 161

The surface area is 161 ft2.

Holt CA Course 1

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

Cylinder

Find the surface area S of the cylinder. Write your answer in terms of .

S = area of curved surface + (2 area of each base)

Substitute 7 for h and 4 for r.

S = (h 2r) + (2 r2)

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

ft

S = (7 2 4)+ (2 16) Simplify the power.

Holt CA Course 1

10-10 Surface AreaAdditional Example 3 Continued

Find the surface area S of the cylinder. Write in terms of .

S = (56 + 32)

The surface area is about 88 ft2.

Multiply.

S = 88

S = 56 + 32

Use the Distributive Property.

Holt CA Course 1

10-10 Surface AreaCheck It Out! Example 1

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

Holt CA Course 1

10-10 Surface AreaCheck It Out! Example 1B Continued

Side: 10 8 = 80

Top: 10 6 = 60

Front: 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

Holt CA Course 1

10-10 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 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

Holt CA Course 1

10-10 Surface AreaCheck It Out! Example 3

Find the surface area S of the cylinder. Write your answer in terms of .

S = area of lateral surface + (2 area of each base)

Substitute 9 for h and 6 for r.

S = (h 2r) + (2 r2)

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

6 ft

9 ft

S = (9 2 6) + (2 36) Simplify the power.

Holt CA Course 1

10-10 Surface AreaCheck It Out! Example 3 Continued

Find the surface area S of the cylinder. Write your answer in terms of .

S = (108 + 72)

S = 180

The surface area is about 180ft2.

Multiply.S = 108 + 72

Use the Distributive Property.

Holt CA Course 1

10-10 Surface AreaLesson Quiz

Find the surface area of each figure. Use 3.14 as an estimate 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