1. 9-3 Volume of Pyramids, Cones, and Spheres Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 9-3 Volume of Pyramids, Cones, and Spheres Warm Up
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Warm Up
Find each volume to the nearest tenth.
Use 3.14 for .
1. cylinder: radius = 6 m, height = 11 m
1,243.4 m3
2. rectangular prism: length = 10 cm,
width = 8.64 cm, height = 12.9 cm
1,114.6 cm3
3. triangular prism: base area = 34 ft2, height = 18 ft
612 ft3
4. cylinder: diameter = 8 m, height = 18 m
904.3 m3

3. 9-3 Volume of Pyramids, Cones, and Spheres Problem of the Day
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Problem of the Day
The volume of a 10-meter-tall square pyramid is 120 m3. What is the length of each side of the base?
6 m

4. 9-3 Learn to find the volume of pyramids, cones, and spheres.
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Learn to find the volume of pyramids, cones, and spheres.

5. 9-3 Volume of Pyramids, Cones, and Spheres
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
If you pour sand from a pyramid-shaped container into a prism-shaped container with the same height, base shape, and base size, you will discover an interesting relationship. The prism-shaped container appears to hold three times as much sand as the pyramid-shaped container.

6. 9-3 Volume of Pyramids, Cones, and Spheres
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
In fact, the volume of a pyramid is exactly one-third the volume of a prism that has the same height, base shape, and base size as the pyramid. The height of a pyramid is the perpendicular distance from the pyramid’s base to its vertex.
VOLUME OF A PYRAMID
The volume V of a pyramid is one-third the area of its base B times its height h.
V = Bh 1 3

7. Additional Example 1A: Finding the Volume of a Pyramid
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Additional Example 1A: Finding the Volume of a Pyramid
Find the volume of the pyramid. A. 1 3
3 ft
V = Bh
Use the formula.
Find the area of the
rectangular base.
B = 5 · 6 = 30
6 ft 1 3
V =
· 30 · 3
Substitute for B and h.
5 ft
V = 30
Multiply.
The volume is 30 ft3.

8. Additional Example 1B: Finding the Volume of the Pyramid
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Additional Example 1B: Finding the Volume of the Pyramid
Find the volume of the pyramid. B. 1 3
V = Bh
Use the formula. 1 2
Find the area of the
triangular base.
B = 2 · 3 = 3 1 3
Substitute for B and h.
V =
· 3 · 5
V = 5
Multiply.
The volume is 5 cm3.

9. 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 1A
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Try This: Example 1A
Find the volume of the pyramid. A. 1 3
4 ft
V = Bh
Use the formula.
Find the area of the
rectangular base.
B = 9 · 7 = 63 1 3
7 ft
V =
· 63 · 4
Substitute for B and h.
9 ft
V = 84
Multiply.
The volume is 84 ft3.

10. 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 1B
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Try This: Example 1B
Find the volume of the pyramid. B. 1 3
V = Bh
Use the formula.
h = 4 m 1 2
Find the area of the
triangular base.
B = 3 · 8 = 12 1 3
Substitute for B and h.
V =
· 12 · 4
3 m
V = 16
Multiply.
h = 8 m
The volume is 16 m3.

11. 9-3 Volume of Pyramids, Cones, and Spheres
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
The volume of a cone is one-third the volume of a cylinder with the same height and a congruent base. The height of a cone is the perpendicular distance from the cone’s base to its vertex.
VOLUME OF A CONE
The volume V of a cone is one-third the area of its base, r2, times its height h.
V = r2h 1 3

12. Additional Example 2: Finding the Volume of a Cone
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Additional Example 2: Finding the Volume of a Cone
Find the volume of a cone to the nearest tenth. Use 3.14 for . 1 3
V =
r2h
Use the formula. 1 3
V 
· 3.14 · 52 · 6
Substitute.
V  157
Multiply.
The volume is about yd3.

13. 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 2
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Try This: Example 2
Find the volume of a cone to the nearest tenth. Use 3.14 for . 1 3
V =
r2h
Use the formula.
3 yd 1 3
V 
· 3.14 · 22 · 3
Substitute.
V  12.56
Multiply.
2 yd
The volume is about 12.6 yd3.

14. 9-3 Volume of Pyramids, Cones, and Spheres VOLUME OF A SPHERE
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
VOLUME OF A SPHERE
The volume V of a sphere is times  times the radius r cubed.
V = r3 4 3 4 3

15. Additional Example 3: Finding the Volume of a Sphere
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Additional Example 3: Finding the Volume of a Sphere
Find the volume of the sphere to the nearest tenth. Use 3.14 for . 4 3
V =
r3
Use the formula. 4 3
V 
· 3.14 · 73
Substitute.
V 
Multiply.
V 
Round.
The volume is about 1,436.0 in3.

16. 9-3 Volume of Pyramids, Cones, and Spheres Try This: Example 3
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Try This: Example 3
Find the volume of the sphere to the nearest tenth. Use 3.14 for . 4 3
V =
r3
Use the formula.
4 in. 4 3
V 
· 3.14 · 43
Substitute.
V 
Multiply.
V  267.9
Round.
The volume is about in3.

17. 9-3 Volume of Pyramids, Cones, and Spheres Lesson Quiz
Course 2
9-3
Volume of Pyramids, Cones, and Spheres
Lesson Quiz
Find the volume of each solid to the nearest tenth. Use 3.14 for .
301.4 yd3
80 ft3
3. sphere with radius 3 ft
4. 14 ft tall triangular pyramid whose base triangle has a 12 ft base and a height of 9 ft
113.0 ft3
252 ft3