volume of cylinders

1. Volume of Prisms and Cylinders
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Lesson QuizzesLesson Quizzes

2. Volume of Prisms and Cylinders
Warm Up
Find the area of each figure described. Use
3.14 for π.
1. a triangle with a base of 6 feet and a height
of 3 feet
2. a circle with radius 5 in.
9 ft2
78.5 in2

3. Volume of Prisms and Cylinders
Problem of the Day
You are painting identical wooden cubes
red and blue. Each cube must have 3
red faces and 3 blue faces. How many
cubes can you paint that can be
distinguished from one another?
only 2

4. Volume of Prisms and Cylinders
Learn to find the volume of prisms and
cylinders.

5. Volume of Prisms and Cylinders

6. Volume of Prisms and Cylinders

7. Volume of Prisms and Cylinders
Area is measured in square units. Volume is
measured in cubic units.
Remember!

8. Volume of Prisms and Cylinders
Find the volume of each figure to the nearest
tenth. Use 3.14 for π.
Additional Example 1A: Finding the Volume of
Prisms and Cylinders
a rectangular prism with base 2 cm by 5 cm and
height 3 cm
= 30 cm3
B = 2 • 5 = 10 cm2
V = Bh
= 10 • 3
Area of base
Volume of a prism

9. Volume of Prisms and Cylinders
Find the volume of the figure to the nearest
tenth. Use 3.14 for π.
4 in.
12 in.
= 192π ≈ 602.9 in3
B = π (42
) = 16π in2
V = Bh
= 16π • 12
Additional Example 1B: Finding the Volume of
Prisms and Cylinders
Area of base
Volume of a
cylinder

10. Volume of Prisms and Cylinders
Find the volume of the figure to the nearest
tenth. Use 3.14 for π.
5 ft
7 ft
6 ft
V = Bh
= 15 • 7
= 105 ft3
B = • 6 • 5 = 15 ft21
2
Additional Example 1C: Finding the Volume of
Prisms and Cylinders
Area of base
Volume of a prism

11. Volume of Prisms and Cylinders
Find the volume of the figure to the nearest
tenth. Use 3.14 for π.
A rectangular prism with base 5 mm by 9 mm and
height 6 mm.
= 270 mm3
B = 5 • 9 = 45 mm2
V = Bh
= 45 • 6
Area of base
Volume of prism
Check It Out: Example 1A

12. Volume of Prisms and Cylinders
Find the volume of the figure to the nearest
tenth. Use 3.14 for π.
8 cm
15 cm
B = π (82
)
= 64π cm2
= (64π)(15) = 960π
≈ 3,014.4 cm3
Check It Out: Example 1B
Area of base
Volume of a cylinderV = Bh

13. Volume of Prisms and Cylinders
Find the volume of the figure to the nearest
tenth. Use 3.14 for π.
10 ft
14 ft
12 ft
= 60 ft2
= 60(14)
= 840 ft3
Check It Out: Example 1C
Area of base
Volume of a prism
B = • 12 • 10
1
2
V = Bh

14. Volume of Prisms and Cylinders
A juice box measures 3 in. by 2 in. by 4 in. Explain
whether tripling the length, width, or height of the
box would triple the amount of juice the box holds.
Additional Example 2A: Exploring the Effects of
Changing Dimensions
The original box has a volume of 24 in3
. You could
triple the volume to 72 in3
by tripling any one of the
dimensions. So tripling the length, width, or height
would triple the amount of juice the box holds.

15. Volume of Prisms and Cylinders
A juice can has a radius of 2 in. and a height of 5
in. Explain whether tripling the height of the can
would have the same effect on the volume as
tripling the radius.
Additional Example 2B: Exploring the Effects of
Changing Dimensions
By tripling the height, you would triple the volume. By
tripling the radius, you would increase the volume to
nine times the original.

16. Volume of Prisms and Cylinders
By tripling the radius,
you would increase the
volume nine times.
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.
Check It Out: Example 2
V = 36π • 3 = 108π cm3
The original cylinder has a volume of 4π • 3 =
12π cm3
.

17. Volume of Prisms and Cylinders
Check It Out: Example 2 Continued
Tripling the height would
triple the volume.
V = 4π • 9 = 36π cm3
The original cylinder has a volume of 4π • 3
= 12π cm3
.

18. Volume of Prisms and Cylinders
A drum company advertises a snare drum that
is 4 inches high and 12 inches in diameter.
Estimate the volume of the drum.
Additional Example 3: Music Application
d = 12, h = 4
r = = = 6
Volume of a cylinder.
d
2V = (πr2
)h
12
2
= (3.14)(6)2
• 4
= (3.14)(36)(4)
= 452.16 ≈ 452
Use 3.14 for π.
The volume of the drum is approximately 452 in3
.

19. Volume of Prisms and Cylinders
A drum company advertises a bass drum that
is 9 inches high and 19 inches in diameter.
Estimate the volume of the drum.
Check It Out: Example 3
d = 19, h = 9
r = = = 9.5
Volume of a cylinder.
d
2V = (πr2
)h
19
2
= (3.14)(9.5)2
• 9
= (3.14)(90.25)(9)
= 2550.465 ≈ 2550
Use 3.14 for π.
The volume of the drum is approximately 2,550 in3
.

20. Volume of Prisms and Cylinders
Find the volume
of the the barn.
Volume of
barn
Volume of
rectangular
prism
Volume of
triangular
prism
+=
= 30,000 + 10,000
V = (40)(50)(15) + (40)(10)(50)
1
2
= 40,000 ft3
The volume is 40,000 ft3
.
Additional Example 4: Finding the Volume of
Composite Figures

21. Volume of Prisms and Cylinders
Check It Out: Example 4
Find the volume of the house.
3 ft
4 ft
8 ft
5 ft
= (8)(3)(4) + (5)(8)(3)
1
2
= 96 + 60
V = 156 ft3
Volume of
house
Volume of
rectangular
prism
Volume of
triangular
prism
+=

22. Volume of Prisms and Cylinders
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems

23. Volume of Prisms and Cylinders
Lesson Quiz
Find the volume of each figure to the nearest
tenth. Use 3.14 for π.
306 in3942 in3
160.5 in3
No; the volume would be quadrupled because
you have to use the square of the radius to find
the volume.
10 in.
8.5 in.3 in.
12 in.12 in.
2 in.
15 in.10.7 in.
1. 3.2.
4. Explain whether doubling the radius of the
cylinder above will double the volume.

24. Volume of Prisms and Cylinders
1. Identify the volume of the cylinder to the
nearest tenth. Use 3.14 for π.
A. 1099 in3
B. 1582.6 in3
C. 1356.5 in3
D. 1846.3 in3
Lesson Quiz for Student Response Systems

25. Volume of Prisms and Cylinders
2. Identify the volume of the rectangular prism to
the nearest tenth.
A. 338 m3
B. 390 m3
C. 364 m3
D. 422.5 m3
Lesson Quiz for Student Response Systems

26. Volume of Prisms and Cylinders
3. Explain whether doubling the height of a
rectangular prism will double the volume.
A. Yes; the volume would be doubled because you
have to use the height to find the volume.
B. No; the volume would be tripled because you
have to use height to find the volume.
C. No; the volume would be tripled because you
have to use the square of the height to find the
volume.
D. Yes; the volume would be doubled because you
have to use the square of the height to find the
volume.
Lesson Quiz for Student Response Systems