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9-3 Volume of Pyramids, Cones, and Spheres
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
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
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
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
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
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
Learn to find the 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.
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.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
VOLUME OF A PYRAMID
The volume V of a pyramid is one-third the area of its base B times its height h.
V = Bh13
Find the volume of the pyramid.
Additional Example 1A: Finding the Volume of a Pyramid
A.V = 1
3Bh Use the formula.
B = 5 · 6 = 30 Find the area of the rectangular base.
V = 13 · 30 · 3 Substitute for B and h.
V = 30
The volume is 30 ft3.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
5 ft6 ft
3 ft
Multiply.
Additional Example 1B: Finding the Volume of the Pyramid
Find the volume of the pyramid.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
B. V = 13
Bh Use the formula.
B = 2 · 3 = 3 Find the area of the triangular base.
V = 13 · 3 · 5
V = 5
The volume is 5 cm3.
Multiply.
Substitute for B and h.
12
·
Find the volume of the pyramid.
Try This: Example 1A
A.V = 1
3Bh Use the formula.
B = 9 · 7 = 63 Find the area of the rectangular base.
V = 13 · 63 · 4 Substitute for B and h.
V = 84
The volume is 84 ft3.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
9 ft7 ft
4 ft
Multiply.
Try This: Example 1B
Find the volume of the pyramid.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
B. V = 13
Bh Use the formula.
B = 3 · 8 = 12 Find the area of the triangular base.
V = 13 · 12 · 4
V = 16
The volume is 16 m3.
Multiply.
Substitute for B and h.
12
·
h = 8 m3 m
h = 4 m
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.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
VOLUME OF A CONE
The volume V of a cone is one-third the area of its base, r2, times its height h.
V = r2h13
Find the volume of a cone to the nearest tenth. Use 3.14 for .
Additional Example 2: Finding the Volume of a Cone
V =13 r2h
V 13 · 3.14 · 52 · 6
V 157
The volume is about 157.0 yd3.
Use the formula.
Substitute.
Multiply.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
Find the volume of a cone to the nearest tenth. Use 3.14 for .
V =13 r2h
V 13 · 3.14 · 22 · 3
V 12.56
The volume is about 12.6 yd3.
Use the formula.
Substitute.
Multiply.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
Try This: Example 2
3 yd
2 yd
VOLUME OF A SPHERE
The volume V of a sphere is times times the radius r cubed.
V = r343
43
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 .
V =43 r3 Use the formula.
Substitute.
Multiply.
V 43 · 3.14 · 73
V 1436.026
V 1436.0
The volume is about 1,436.0 in3.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
Round.
Try This: Example 3
Find the volume of the sphere to the nearest tenth. Use 3.14 for .
V =43 r3 Use the formula.
Substitute.
Multiply.
V 43 · 3.14 · 43
V 267.946
V 267.9
The volume is about 267.9 in3.
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
4 in.
Round.
Lesson Quiz
Course 2
9-3 Volume of Pyramids, Cones, and Spheres
Find the volume of each solid to the nearest tenth. Use 3.14 for .
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
1. 2.
80 ft3
301.4 yd3
113.0 ft3
252 ft3
