8-11 Surface Area of Pyramids and Cones

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Problem of the DayProblem of the Day

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8-11 Surface Area of Pyramids and Cones

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Find the perimeter or circumference of each figure. Use 3.14 for .

1. 2.

30 cm 138.16 ft

8-11 Surface Area of Pyramids and Cones

Problem of the DayIn a survey, 69 people were asked whether they prefer hamburgers or hot dogs. Thirty-three people said they prefer hot dogs. What percent of the people surveyed said they prefer hamburgers?

about 52%

8-11 Surface Area of Pyramids and Cones

MA.7.G.2.1 Justify and apply formulas for surface area..of…pyramids…and cones.Also MA.7.G.2.2

Sunshine State Standards

8-11 Surface Area of Pyramids and Cones

Vocabulary

regular pyramid

slant height of a pyramidslant height of a cone

8-11 Surface Area of Pyramids and Cones

The diagram shows a square pyramid. The blue dashed line labeled l is the slant height of the pyramid, the distance from the vertex to the midpoint of an edge of the base.

The base of a regular pyramid is a regular polygon, and the faces are congruent isosceles triangles.

8-11 Surface Area of Pyramids and Cones

8-11 Surface Area of Pyramids and Cones

Additional Example 1A: Finding the Surface Area of a Pyramid

Find the surface area of the pyramid.

S = 81 + 180

S = 261 m2

S = B + Pl12

S = (9 • 9) + (36)(10)12

Use the formula.

S = lw + Pl12

B = lw

Substitute. P = 4(9) = 36

Add.

The surface area is 261 square meters.

8-11 Surface Area of Pyramids and Cones

Additional Example 1B: Finding the Surface Area of a Pyramid

Find the surface area of the pyramid.

S = 21 + 84

S = 105 in2

S = B + Pl12 Use the formula.

B= ½bh.

Substitute. P = 3(7) = 21

Add.

S = bh + Pl12

12

S = (7)(6) + (21)(8)12

12

The surface area is 105 square inches.

8-11 Surface Area of Pyramids and Cones

Check It Out: Example 1A

Find the surface area of the pyramid.

S = 9 + 30

S = 39 m2

S = B + Pl12

S = (3 • 3) + (12)(5)12

Use the formula.

B= lw.

Substitute. P = 4(3) = 12

Add.

5 m

3 m3 m

S = lw + Pl12

The surface area is 39 square meters.

8-11 Surface Area of Pyramids and Cones

Check It Out: Example 1B

Find the surface area of the pyramid

S = 6 + 36

S = 42 in2

S = B + Pl12 Use the formula.

B= ½bh.

Substitute. P = 3(4) = 12

Add.

S = bh + Pl12

12

S = (4)(3) + (12)(6)12

12

4 in.

3 in.4 in.

6 in.

4 in.

The surface area is 42 square inches.

8-11 Surface Area of Pyramids and Cones

The diagram shows a cone and its net. The blue dashed line is the slant height of the cone, the distance from the vertex to a point on the edge of the base.

8-11 Surface Area of Pyramids and Cones

8-11 Surface Area of Pyramids and Cones

Additional Example 2: Finding the Surface Area of a Cone

Find the surface area of the cone. Use 3.14 for .

Use the formula.

S ≈ 122.46

S = r2 + rl

S ≈ (3.14)(32) + (3.14)(3)(10)

S ≈ 28.26 + 94.2

The surface area is about 122.46 square centimeters.

Substitute.

Multiply.

Add.

8-11 Surface Area of Pyramids and Cones

Check It Out: Example 2

Find the surface area of the cone. Use 3.14 for .

Use the formula.

S ≈ 175.84

S = r2 + rl

S ≈ (3.14)(42) + (3.14)(4)(10)

S ≈ 50.24 + 125.6

The surface area is about 175.84 square centimeters.

Substitute.

Multiply.

Add.

8-11 Surface Area of Pyramids and Cones

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

8-11 Surface Area of Pyramids and Cones

Lesson Quiz

1. Find the surface area of the pyramid.

2. Find the surface area of the cone. Use 3.14 for .219.8 ft2

236.25 m2

3. A house being built is to have a roof in the shape of a square pyramid. The sides of the square base are 21 feet long and the slant height will be 12 feet. What will the surface area of the roof be? (Hint: The base of the pyramid is not part of the roof.) 504 ft²

8-11 Surface Area of Pyramids and Cones

1. Find the surface area of a regular pyramid with a base of 12 feet by 12 feet and a slant height of 14 feet.

A. 2016 ft2

B. 816 ft2

C. 480 ft2

D. 240 ft2

Lesson Quiz for Student Response Systems

8-11 Surface Area of Pyramids and Cones

2. Find the surface area of a cone with a radius of 3 feet and a slant height of 6 feet. Use 3.14 for . A. 18 ft2

B. 56.52 ft2

C. 75.36 ft2

D. 84.78 ft2

Lesson Quiz for Student Response Systems