1. Warm-up The base length is 30 cm.
EQ: How do I solve real world problems involving cylinders, cones, and spheres?
Warm-up
1.) Find the missing side. The height of the triangle is 20 inches.
25 cm
25 cm
The base length is 30 cm.
x cm

2. A cylinder is a three-dimensional figure that has two congruent circular bases.

3. Volume of Cylinders Words Numbers Formula
Cylinder: The volume of a cylinder is the area of the base B times the height h.
B =  (22)
V = Bh
= 4 units2
V = (r2)h
V = (4)(6) = 24
 75.4 units3

4. Area is measured in square units. Volume is measured in cubic units.
Remember!

5. Example 1: Finding the Volume of Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for .
Volume of a cylinder formula
V =  r2 h
4 in.
V =  • 42 • 12
Substitute
12 in.
Solve
V =  • 16 • 12
V = 192
V  in3
Terms of pi

6. Example 2: Volume of Cylinders
Find the volume of the figure to the nearest tenth. Use 3.14 for .
B =  (82)
Area of base
8 cm
= 64 cm2
V = Bh
Volume of a cylinder
15 cm
= (64)(15) = 960
 3,014.4 cm3

7. Example 3: Volume of Cylinders
A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume.
The original cylinder has a volume of 4 • 3 = 12 cm3.
V = 36 • 3 = 108 cm3
By tripling the radius, you would increase the volume nine times.

8. Check It Out: Example 2B Continued
The original cylinder has a volume of 4 • 3 = 12 cm3.
V = 4 • 9 = 36 cm3
Tripling the height would triple the volume.

9. Example 4: Volume of Cylinders
A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum.
d = 12, h = 4
d 2
r = = = 6
V = (r2)h
Volume of a cylinder.
= (3.14)(6)2 • 4
Use 3.14 for p.
= (3.14)(36)(4)
= ≈ 452
The volume of the drum is approximately 452 in.2

10. Example 5: Volume of Cylinders
A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum.
d = 28, h = 12
d 2
r = = = 14
V = (r2)h
Volume of a cylinder.
= (3.14)(14)2 • 12
Use 3.14 for .
= (3.14)(196)(12)
= ≈ 7,385
The volume of the drum is approximately 7,385 in.2

11. Lesson Quiz
Find the volume of each figure to the nearest tenth. Use 3.14 for .
10 in. 1.
12 in.
942 in3