Hmh alg1 mod7 1 volume of prisms & cylinders (1)

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

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

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

Learn to find the volume of prisms and
cylinders.

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

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

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

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
Area of base
Volume of a prism

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

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

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

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.

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.

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
.

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
.

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
.

A drum company advertises a bass drum that
is 9 inches high and 19 inches in diameter.
Estimate the volume of the drum.
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
.

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

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
+=

Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems

Lesson Quiz
Find the volume of each figure to the nearest
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.

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

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

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.

Hmh alg1 mod7 1 volume of prisms & cylinders (1)

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