8-9 Volume of Pyramids and Cones

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

8-9 Volume of Pyramids and Cones

Warm UpFind each volume to the nearest tenth. Use 3.14 for .

1. cylinder: radius = 6 m, height = 11 m

1,243.4 m3

1,114.6 cm3

612 ft3

904.3 m3

2. rectangular prism: length = 10 cm, width = 8.64 cm, height = 12.9 cm

3. triangular prism: base area = 34 ft2, height = 18 ft

4. cylinder: diameter = 8 m, height = 18 m

8-9 Volume of Pyramids and Cones

Problem of the DayWhen my age is divided by 2, 3, 4, or 6 there is always a remainder of 1, but when it is divided by 7 there is no remainder. How old am I?49

8-9 Volume of Pyramids and Cones

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

Sunshine State Standards

8-9 Volume of Pyramids and Cones

Suppose you have a square-pyramid-shaped container and a square-prism-shaped container, and the bases and heights are the same size. If you pour sand from the pyramid into the prism, it appears that the prism holds three times as much sand as the pyramid.

8-9 Volume of Pyramids and Cones

In fact, the volume of a pyramid is exactly one-third the volume of a prism with the same height and a congruent base.

The height of a pyramid is the perpendicular distance from the pyramid’s base to the vertex opposite the base.

8-9 Volume of Pyramids and Cones

Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable.

Additional Example 1A: Finding the Volume of a Rectangular Pyramid

V = 13

Bh Use the formula.

B = 5 · 7 = 35Find the area of the rectangular base.

V = 13

· 35 · 4 Substitute for B and h.

V ≈ 46.7 ft3

Estimate

5 ft 7 ft

4 ft

Multiply.

V = 13

· 30 · 5 Round the measurements.

V = 50 ft3 The answer is reasonable.

8-9 Volume of Pyramids and Cones

Find the volume of the pyramid to the nearest tenth. Estimate to check whether the answer is reasonable.

Additional Example 1B: Finding the Volume of a Rectangular Pyramid

V = 13

Bh Use the formula.

B = ½ · 30 · 25 = 375Find the area of the triangular base.

V = 13

· 375 · 26 Substitute for B and h.

V = 3250 ft3 Multiply.

8-9 Volume of Pyramids and Cones

Find the volume of each pyramid to the nearest tenth. Estimate to check whether the answer is reasonable.

Check It Out: Example 1A

8-9 Volume of Pyramids and Cones

Check It Out: Example 1A

V = 13

Bh

V ≈ 74.7

Estimate.

V ≈ 13

· 54 · 4

≈ 72

13

= (8)(7)(4)

about 74.7 ft3

The answer is reasonable

8-9 Volume of Pyramids and Cones

Find the volume of each pyramid to the nearest tenth. Estimate to check whether the answer is reasonable.

Check It Out: Example 1B

8-9 Volume of Pyramids and Cones

Check It Out: Example 1B Continued

V = 13

Bh

Estimate.

V ≈ 13

· 84 · 12

≈ 336

13

B= (9)(19) = 85.5

≈ 342 m

The answer is reasonable

13 (85.5)(12) = 342V ≈

2

8-9 Volume of Pyramids and Cones

The volume of a cone is one-third the volume of a cylinder with the same height and a congruent base.

8-9 Volume of Pyramids and Cones

Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable.

Additional Example 2A: Finding the Volume of a Cone

V =13 Bh

V 13 · 78.5 · 6

V 157 yd3

Estimate

Use the formula. The base is a circle so B = · r2 3.14 · 52 78.5.

Substitute for B and h.

Multiply.

13

· ≈ 1.13V ≈ · 52 · 6

150 yd3 The answer is reasonable.

8-9 Volume of Pyramids and Cones

Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable.

Additional Example 2B: Finding the Volume of a Cone

V =13 Bh

V 13 · 28.26 · 7

V 65.9 cm3

Estimate

Use the formula. The base is a circle so B = · r2 3.14 · 32 28.26.

Substitute for B and h.

Multiply.

13

· ≈ 1.13V ≈ · 32 · 7

63 cm3 The answer is reasonable.

7 cm

3 cm

8-9 Volume of Pyramids and Cones

Find the volume of the cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable.

Check It Out: Example 2

7 cm

4 cm

V =13

V 29.31about 29.3 cm3

Estimate:

13

V ≈ · 22 7

28

r2h (3.14)(2)2(7)13

The answer is reasonable.

8-9 Volume of Pyramids and Cones

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

8-9 Volume of Pyramids and Cones

Lesson QuizFind the volume of each pyramid or cone to the nearest tenth. Use 3.14 for . Estimate to check whether the answer is reasonable.

3.

1. 2.

80 ft3

301.4 yd3

252 ft3

8-9 Volume of Pyramids and Cones

1. Identify the volume of the prism.

A. 576 ft3

B. 288 ft3

C. 96 ft3

D. 24 ft3

Lesson Quiz for Student Response Systems

8-9 Volume of Pyramids and Cones

2. Identify the volume of cone to the nearest tenth. Use 3.14 for .

A. 4240.0 in3

B. 3815.1 in3

C. 1271.7 in3

D. 141.3 in3

Lesson Quiz for Student Response Systems

8-9 Volume of Pyramids and Cones

3. Identify the volume of the pyramid.

A. 1632 ft3

B. 544 ft3

C. 192 ft3

D. 27 ft3

Lesson Quiz for Student Response Systems