1. Volume of Pyramids and Cones
6-7
Volume of Pyramids and Cones
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. Volume of Pyramids and Cones
Pre-Algebra
6-7
Volume of Pyramids and Cones
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 p.
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
55.4 ft3

3. 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

4. Learn to find the volume of pyramids and cones.

5. Vocabulary
pyramid
cone

6. A pyramid is named for the shape of its base
A pyramid is named for the shape of its base. The base is a polygon, and all of the other faces are triangles. A cone has a circular base. The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.

7. VOLUME OF PYRAMIDS AND CONES
(22)

8. Additional Example 1A: Finding the Volume of Pyramids and Cones
Find the volume of the figure. A.
B = (4 • 7) = 14 cm2 1 2 1 3
V = • 14 • 6
V = Bh 1 3
V = 28 cm3

9. Additional Example 1B: Finding the Volume of Pyramids and Cones
Find the volume of the figure. B.
B = (32) = 9 in2 1 3
V = • 9 • 10
V = Bh 1 3
V = 30  94.2 in3
Use 3.14 for .

10. Additional Example 1C: Finding the Volume of Pyramids and Cones
Find the volume of the figure. C.
B = 14 • 6 = 84 m2 1 3
V = • 84 • 10
V = Bh 1 3
V = 280 m3

11. Try This: Example 1A
Find the volume of the figure. A.
B = (5 • 7) = 17.5 in2 1 2
7 in. 1 3
V = • 17.5 • 7
V = Bh 1 3
5 in.
7 in.
V  40.8 in3

12. Try This: Example 1B
Find the volume of the figure. B.
B = (32) = 9 m2
7 m 1 3
V = • 9 • 7
V = Bh 1 3
3 m
V = 21  65.9 m3
Use 3.14 for .

13. Try This: Example 1C
Find the volume of the figure. C.
B = 4 • 4 = 16 ft2
8 ft 1 3
V = • 16 • 8
V = Bh 1 3
4 ft
4 ft
V  42.7 ft3

14. Additional Example 2: Exploring the Effects of Changing Dimensions
A 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.

15. Try This: Example 2
A 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 3
V = pr2h
= p(22)5
 m3
V = pr2 (2h)
= p(22)(2•5)
= p(2 • 2)2(5)
V = p (2r)2h
 m3
 m3
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.

16. Additional Example 4: 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
A = bh 1 3
V = (3025)(24)
V = Bh 1 3
V = 24,200 m3

17. Try This: Example 4
Find the volume of a pyramid with a height of 12 m and a base with 48 m sides.
B = 482 = 2304 m2
A = bh 1 3
V = (2304)(12)
V = Bh 1 3
V = 9216 m3

18. 1. the triangular pyramid
Lesson Quiz: Part 1
Find the volume of each figure to the nearest tenth.Use 3.14 for p.
1. the triangular pyramid
2. the cone

19. Lesson Quiz: Part 2
Find the volume of each figure to the nearest tenth.Use 3.14 for p.
3. Explain whether tripling the height of a square pyramid would triple the volume.

20. 1. the triangular pyramid 6.3 m3
Lesson Quiz: Part 1
Find the volume of each figure to the nearest tenth.Use 3.14 for p.
1. the triangular pyramid
6.3 m3
2. the cone
78.5 in3

21. Lesson Quiz: Part 2
Find the volume of each figure to the nearest tenth.Use 3.14 for p.
3. Explain whether tripling the height of a square pyramid would triple the volume.
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.