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Course 3
Volume of Cylinders, Cones, and Spheres
Warm UpFind the area of each figure described. Use 3.14 for pi.
1.
2. a circle with radius 5 in.
Course 3
Volume of Cylinders, Cones, and Spheres
VOLUME OF CYLINDERSWords Numbers Formula
Cylinder: The volume of a cylinder is the area of the base B times the height h.
B = (22)= 4 units2
V = (4)(6) = 24 75.4 units3
V = Bh
= (r2)h
Area is measured in square units. Volume is measured in cubic units.
Remember!
Course 3
Volume of Cylinders, Cones, and Spheres
Find the volume of the figure to the nearest tenth. Use 3.14 for .
4 in.
12 in.
= 192 602.9 in3
B = (42) = 16 in2
V = Bh
= 16 • 12
Additional Example 1B: Finding the Volume of Prisms and Cylinders
Area of base
Volume of a cylinder
Course 3
Volume of Cylinders, Cones, and Spheres
Find the volume of the figure to the nearest tenth. Use 3.14 for .
8 cm
15 cm
B = (82)
= 64 cm2
= (64)(15) = 960
3,014.4 cm3
Check It Out: Example 1B
Area of base
Volume of a cylinderV = Bh
Course 3
Volume of Cylinders, Cones, and Spheres
Find the volume of each figure to the nearest tenth. Use 3.14 for π.
10 in.
12 in.
1.
2. Explain whether doubling the radius of the cylinder above will double the volume.
Course 3
Volume of Cylinders, Cones, and Spheres
VOLUME OF CONES
Course 3
Volume of Cylinders, Cones, and Spheres
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 .
Find the volume of the figure. Use 3.14 for .
Course 3
Volume of Cylinders, Cones, and Spheres
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
Find the volume of the figure. Use 3.14 for .
Course 3
Volume of Cylinders, Cones, and Spheres
Lesson Quiz: Part 1
Find the volume of each figure to the nearest tenth. Use 3.14 for .
78.5 in3
2. the cone
Course 3
Volume of Cylinders, Cones, and Spheres
A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphere is a great circle.
Course 3
Volume of Cylinders, Cones, and Spheres
The volume of a hemisphere is exactly halfway between the volume of a cone and a cylinder with the same radius r and height equal to r.
Course 3
Volume of Cylinders, Cones, and Spheres
Course 3
Volume of Cylinders, Cones, and Spheres
Additional Example 1: Finding the Volume of a Sphere
Find the volume of a sphere with radius 12 cm, both in terms of and to the nearest tenth. Use 3.14 for .
= 2304 cm3 7,234.6 cm3
Volume of a sphere
Substitute 12 for r.
43
V = r3
= (12)343
Course 3
Volume of Cylinders, Cones, and Spheres
Check It Out: Example 1
Find the volume of a sphere with radius 3 m, both in terms of and to the nearest tenth. Use 3.14 for .
= 36 m3 113.0 m3
Volume of a sphere
Substitute 3 for r.
43
V = r3
= (3)343
Course 3
Volume of Cylinders, Cones, and Spheres
Lesson Quiz: Part I
Find the volume of each sphere, both in terms of and to the nearest tenth. Use 3.14 for .
1. r = 4 ft
2. d = 6 m 36m3, 113.0 m3
85.3ft3, 267.8 ft3
3. A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume?
Course 3
Volume of Cylinders, Cones, and Spheres
Find the volume of each figure. Use 3.14 for .
1.Cylinder with a height of 3 in and a radius of 2 in
2.Cone with a height of 3 in and a radius of 2 in
3.Sphere with a radius of 2 in
Homework: Workbook pages 60-61, 64
(VOLUME of cylinders, cones, and spheres ONLY)
