Name
Date
Volume of Prisms and Cylinders
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Essential question: How can you solue problems using theformulafor the
uolume of a cylinder?
A cylinder has two parallel congruent circular bases. The area of a base is
rf
.
O ;m'ilT-tt', votume of a Gyrinder
Find the volume of each cylinder. Round your answers to the nearest
tenth if necessary. Use 3.14 for r.
A
A cylindrical oatmeal canister has a radius of 3 inches and a height
of l0 inches.
V: rrfh
' '..
2
=
3.14
Sub
= 3.I4
=
stitute into
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the
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f
=
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B
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in3.
A drink can has a diameter of 6.4 centimeters and a height
of l3 centimeters.
-
First, find the radius:
cm.
12.m
-
V: rfh
2
=
=
x 3.\4
c
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5
=
-
-
3.14
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a\
Muhiply.
The volume of the canister is about
c
formula.
Simplifu the exponent.
ins
1,l.:
r'.,:.1,::..i
,,.l:r:
\- b.4 cm
Substitute into the formula.
-
Simplifu the exponent.
cm3
Multiply.
The volume of the can is about
cm3
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Chapter 6
235
Lesson 2
Find the volume of each figure. Round your answers to the nearest tenth
if necessary. Use 3.14 for r.
12 ft
1.
13
f''.
ft
ta
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.. J:Oft-:
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volume of
2,797.74 cm3. It is 11 cm high. \Mhat is
the length of the radius of its base?
The area of the circular base of a can of
dog food is 12.5 in2. The can is 6 inches
high. \tVhat is its volume?
A can of soup has
6.
A cookie container is in the shape of a
cylinder. Its diameter is 9 inches and its
height is 3 inches. To the nearest cubic
inch, what is its volume?
a
The volume of a rooftop cylindrical water
tank is 1,493 ft3. The tank is 30 feet high.
To the nearest square foot, what is the
area of its base?
cylindrical layers, and each layer is 5 inches tall. The top
layer has a I2-inch diameter. Each of the other layers has a diameter 2 inches
greater than the layer above it. To the nearest cubic inch, what is the cake's volume?
7. A cake has three
(9
-
How is finding the volume of a cylinder like finding the volume of a prism?
c
@
f
How is it different?
l
+
=
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c
!
c
5
A cylinder and a prism both have the same base area and height. l4/hich has
f
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the greater volume?
a)
3
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l
\.A/hich gives a cylinder greater volume: a radius of 16 cm and a height of 20 cn:,
or a radius of 20 cm and a height of 16 cm? Explain.
11. Error Analysis Diane says that tripling the diameter
of the base of a can of soup
increase its volume by a factor of 6. Is she correct? Explain.
Chapter 6
236
will
Lesson 2
Date
Additional Practice
Find the volume of each figure to the nearest tenth.
Use 3.14lor n
1. o.bct
3.
4.
4mm
tl|
tl
17.5 mm
6in
t-----*i
'l
1 in.
5. A cylinder has a diameter of 8 feet and height of 40 feet.
tr
6. A cylinder has a diameter of 16 meters and height of 4 meters.
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3
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f
;
7. A cylindrical paint can is 19 centimeters tall and has a radius of
8 centimeters. What is the volume of the paint can? Round your
answer to the nearest tenth.
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l
B. A cylinder has a radius of 6 ft and a height of 25 ft. Explain
whether tripling the height will triple the volume of the cylinder.
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Chapter 6
237
Practice and Problem Solving
Problem Solvin
A rectangular box is 2 inches high, 3.5 inches wide and
4 inches long. A cylindrical box is 3.5 inches high and has
a diameter of 3.2 inches. Use 3.14lor a. Round to the nearest
tenth.
2. How much bigger is the larger box?
1. Which box has a larger volume?
Use 3.14 for n. Choose the letter for the best answer'
4. How many cubic feet of air are in a
3. A can has diameter of 9.8 cm and
room that is 15 feet long, 10 feet
13.2 cm tall. What is the capacity
wide and B feet high?
the can? Round to the nearest tenth.
F 33ft3
A 203.1 cm3
is
of
c 1200 ft3
H 1500 ft3
J 3768 ft3
B 995.2 cm3
C 3980.7 cm3
D 959.2 cm3
6. A child's wading pool has a diameter
of 5 feet and a height of 1 foot. How
much water would it take to fill the
pool? Round to the nearest gallon.
(Hint: 1 cubic foot of water is
5. How many gallons of water will the
water trough hold? Round to the
nearest gallon. (Hint: 1 cubic foot of
water is approximately 7.5 gallons.)
z1l
approximately 7.5 gallons.)
F
79 gallons
G 589 gallons
H 59 gallons
J
A
B 71 gallons
C 141 gallons
19 gallons
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f
o
f
147 gallons
_=
f
T
o
c
f,
c
5
D 565 gallons
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3
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Chapter 6
238
Practice and Problem Solving