Back to Lesson 10-6
Name
Name
10-5B
6.
7.
8.
Questions on SPUR Objectives
See Student Edition pages 642–645 for objectives.
In 1−3, find the volume of the sphere. Solid dots are the centers of their
respective circles.
1.
e
2.
6
3.
s
s
regular pentagonal pyramid
8
regular square pyramid
L.A. = _52s
8 in.
cube
L.A. = 2s
L.A. = 4e2
2048
___
π≈
10.
11.
3p
12 cm
288π ≈
2144.661 in
904.779 cm3
4. The volume of a sphere is 12.8 m . Find its diameter.
3
In 9–11, write a formula for the given measure.
9.
Lesson Master
SKILLS Objective C
4000
___
π ≈ 4188.790
3
3
about 2.902 m
3
128,000
_____
π ≈ 134,041.290 m3
2m
k
surface area of right cone
5. The circumference of a hemisphere is 80π. Find its volume. 3
h
m
d
lateral area of right cylinder
USES Objective J
volume of right cylinder
S.A. = 3πkp + πk2 L.A. = 4πm2
V = _π4 d2h
6. The radius of Earth is approximately 3863 miles. Find the
volume of Earth to the nearest thousand cubic miles.
PROPERTIES Objective E
a. How must their heights be related for them to have the same volume?
The height of the cone must be three times
the height of the cylinder.
b. How must the slant height of the cone be related to the height of the cylinder for them to have
the same lateral surface area?
The slant height of the cone must equal
twice the height of the cylinder.
13. Pictured at the right is a square
pyramid sitting on a box of the same
height. What is the ratio of the
volume of the pyramid to the volume
of the box?
241,469,751,000 mi3
7. The town of West Waterford is building
a water tower with the top in the shape
of a sphere. It needs to hold 40,000 gallons
of water. What will be the diameter of the
tank, to the nearest tenth of a foot?
1 ft3 = 7.48 gallons.
12. A right cone and a cylinder have the same base.
518
10-6A
page 2
21.7 ft
5427.8 cm3,
5669.0 cm3
8. The circumference of an official size soccer ball must be between
68.5 and 69.5 centimeters. What are the least and greatest
possible volumes of the ball?
9. Laurel makes glass beads for jewelry. One of her standard beads is a
sphere 12 mm in diameter with a 2 mm-diameter hole running through
the center for a string.
a. Find the volume of glass in the bead.
276π ≈ 867.080 mm3 = 0.867 cm3
x
b. If she has 50 cubic centimeters of molten glass, how many beads
can she make?
1 to 3
x
57 beads
Geometry
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Name
10-6B Lesson Master
Questions on SPUR Objectives
10-6B
page 2
See Student Edition pages 642–645 for objectives.
SKILLS Objective C
In 7–10, give the radius of the sphere with the given volume. Round inexact
answers to the nearest tenth.
r
1. Refer to the sphere and the cylinder containing two cones
shown at the right.
32
7. __
π cubic units
3
r
a. Inside the cylinder, shade the space that has the same
volume as the sphere.
2 units
2r
9. 52 ft3
2.3 ft
r
b. Complete the following. Given a cylinder with radius r and
height 2r containing two cones each with radius r and
height r, the volume of a sphere with radius r is equal to
8. 288π in3
6 in.
10. 1262 m3
6.7 m
USES Objective J
the cylinder minus
the volume of the two cones .
the volume of
11. Find the volume of each ball.
≈ 137 cm3
≈ 29 cm3
≈ 219 cm3
a. tennis ball, 6.4 cm in diameter
b. table-tennis ball, 3.8 cm in diameter
In 2–4, draw the sphere with the given dimension. Then find its volume.
2. radius = 18 mm
3. radius = 1.5 cm
4. diameter = 1 inch
c. baseball, 23.5 cm in circumference
Copyright © Wright Group/McGraw-Hill
12. A tank full of 15,000 in3 of air is to be used to inflate a beach
ball with diameter 20 in., a basketball with diameter 9.5 in.,
and a volleyball with diameter 8 in. Does the tank contain
enough air to fill all of the balls?
7776π ≈
24,429.0 mm3 4.5π ≈ 14.1 cm3 _16 π ≈ 0.5 in3
5. The radius of a sphere is 26 inches.
a. Find the volume of the sphere to the nearest cubic inch.
b. Find the volume of the sphere to the nearest tenth of a
cubic foot.
73,622 in3
42.6 ft3
yes
13. How many ounces of water are displaced if 120 glass marbles
are dropped into a 20-gallon aquarium, and the diameter of
each marble is __12 in.? (1 gallon = 231 cubic inches,
1 pint = 16 fluid ounces, 1 quart = 32 fluid ounces)
14. The diameter of an inflatable beach ball is 16 in. If a person
blowing it up exhales 120 cubic inches of carbon dioxide
with each breath, how many breaths will it take to fill the ball?
15. A globe with a 16-cm radius just fits into a cube-shaped
container. The rest of the container is filled with liquid.
What is the volume of the liquid?
≈ 4.35 oz
≈ 18 breaths
≈ 15,611 cm3
6. The circumference of a great circle of a sphere is 28π cm.
What is its volume?
10,976
____
π ≈ 11,494 cm3
3
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