Volume of Pyramids and Cones 9-6 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

Volume of Pyramids and Cones9-6

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm Up

1. Find the volume of a rectangular prism that is 4 in. tall, 16 in. wide, and 48 in deep.

2. A cylinder has a height of 4.2 m and a diameter of 0.6 m. To the nearest tenth of a cubic meter, what is the volume of the cylinder? Use 3.14 for .

3. A triangular prism’s base is an equilateral triangle. The sides of the equilateral triangle are 4 ft, and the height of the prism is 8 ft. To the nearest cubic foot, what is the volume of the prism?

3072 in3

1.2 m3

55 ft3


Problem of the Day

A ream of paper (500 sheets) forms a rectangular prism 11 in. by 8.5 in. by 2 in. What is the volume of one sheet of paper?0.374 in3


Prep for MA.8.G.5.1 Compare, contrast, and convert units of measure between different measurement systems…and dimensions including…volume, and derived units to solve problems.Rev MA.7.G.2.1

Sunshine State Standards




Additional Example 1A: Finding the Volume of Pyramids and Cones

Find the volume of the figure. Use 3.14 for .

13V = • 14 • 6

V = 28 cm3

V = Bh13

B = (4 • 7) = 14 cm2 12


Additional Example 1B: Finding the Volume of Pyramids and Cones

13V = • 9 • 10

V = 30 94.2 in3

V = Bh13

B = (32) = 9 in2

Use 3.14 for .



Check It Out: Example 1A

13V = • 17.5 • 7

V 40.8 in3

V = Bh13

B = (5 • 7) = 17.5 in2 12

5 in.

7 in.

7 in.



13V = • 9 • 7

V = 21 65.9 m3

V = Bh13

B = (32) = 9 m2

Use 3.14 for .

Check It Out: Example 1B

7 m

3 m


Volume of Pyramids and Cones9-6Additional Example 2: Exploring the Effects of Changing

DimensionsA cone has a radius of 3 ft. and a height of 4 ft. Explain whether tripling the height would have the same effect on the volume of the cone as tripling the radius.

When the height of the cone is tripled, the volume is tripled. When the radius is tripled, the volume becomes 9 times the original volume.


Check It Out: Example 2A cone has a radius of 2 m and a height of 5 m. Explain whether doubling the height would have the same effect on the volume of the cone as doubling the radius.

Double the Radius

Double the Height

Original Dimensions

1

3V = r2h

1

3

1

31

3= (22)5

20.93 m3

1

3V = r2 (2h)

= (22)(2•5) = (2 • 2)2(5)

V = (2r)2h

41.87 m3 83.73 m3

1

3

When the height of a cone is doubled, the volume is doubled. When the radius is doubled, the volume is 4 times the original volume.


Additional Example 3: Social Studies Application

The Pyramid of Kukulcán in Mexico is a square pyramid. Its height is 24 m and its base has 55 m sides. Find the volume of the pyramid.

B = 552 = 3025 m2 13

V = (3025)(24)

V = 24,200 m3

A = bh

V = Bh13

A lowercase b is used to represent the length of the base of a two-dimensional figure. A capital B is used to represent the area of the base of a solid figure.

Caution!


Check It Out: Example 3

B = 482 = 2304 m2 13

V = (2304)(12)

V = 9216 m3

A = bh

V = Bh13

Find the volume of a pyramid with a height of 12 m and a base with 48 m sides.


Additional Example 4: Using a Calculator to Find Volume

Use a calculator to find the volume of a cone to the nearest cubic centimeter if the radius of the base is 15 cm and the height is 64 cm.

Use the pi button on your calculator to find the area of the base.

2ND ^ X2 ENTER

Next, with the area of the base still displayed, find the volume of the cone.

15

64 ( )1 3÷ ENTER

The volume of the cone is approximately 15,080 cm3.

B = r2

V = Bh13


Check It Out: Example 4

Use a calculator to find the volume of a cone to the nearest cubic centimeter if the radius of the base is 14 cm and the height is 16 cm.

Use the pi button on your calculator to find the area of the base.

2ND ^ X2 ENTER

Next, with the area of the base still displayed, find the volume of the cone.

14

16 ( )1 3÷ ENTER

The volume of the cone is approximately 3,282 cm3.

B = r2

V = Bh13


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

Find the volume of each figure to the nearest tenth. Use 3.14 for .

78.5 in3

6.3 m3

1. the triangular pyramid

2. the cone


Lesson Quiz: Part II

Find the volume of each figure to the nearest tenth. Use 3.14 for .

Yes; the volume is one-third the product of the base area and the height. So if you triple the height, the product would be tripled.

3. Explain whether tripling the height of a square pyramid would triple the volume.


1. Identify the volume of the triangular pyramid rounded to the nearest tenth.

A. 16 m3

B. 16.5 m3

C. 17 m3

D. 17.5 m3



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

A. 183.2 in3

B. 176.5 in3

C. 167.2 in3

D. 128.2 in3



3. Explain whether doubling the length of the following rectangular pyramid would double the volume.

A. Yes; the volume is one-third the product of the base area and the height. So if you double the length of the base, the product would be doubled.

B. No; the volume is one-third the product of the base area and the height. So if you double the length of the base, the product would be quadrupled.


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Volume of Pyramids and Cones 9-6 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes