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Lesson 9.1 Skills Practice
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Drum Roll, Please!Volume of a Cylinder
VocabularyExplain why the term describes each given figure.
1. cylinder
2. right circular cylinder
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3. radius and height of the cylinder
h
r
Problem SetIdentify the radius, diameter, and height of each cylinder.
1. 8 cm
10 cm
2. 7 m
15 m
Radius: 4 cm
Diameter: 8 cm
Height: 10 cm
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3. 12 ft
12 ft
4. 20 in.
9 in.
5. 7 mm
8 m
m
6. 4 yd
12 yd
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Calculate and use the area of the base to determine the volume of each given cylinder. Use 3.14 for π.
7.
5 cm
2 cm
The area of each base is π ? 22 < 3.14 ? 4 < 12.56 cm2.
The volume is 12.56 ? 5 < 62.80 cm3.
8.
3 cm
3 cm
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9.
7 ft
8 ft
10.
12 yd
4 yd
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11.
3.5 cm
10 cm
12.
9 ft
5 ft
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Calculate the volume of each cylinder. Use 3.14 for π. Round decimals to the nearest tenth, if
necessary.
13. 5.5 m
7 m
14. 30 yd
22 yd
V 5 πr 2h
V 5 π(5.5)2(7)
V 5 211.75π
V < 664.9 m3
15. 20 m
5 m
16. 10 ft
4.5 ft
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17. 4 mm
6 mm
18. 16 ft
5 ft
19. 9 m
12 m
20. 3.5 cm
13 cm
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Piling On!Volume of a Cone
VocabularyDraw a diagram to illustrate each key term.
1. cone (identify the vertex and the base)
2. height of a cone
Lesson 9.2 Skills Practice
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Problem SetIdentify the radius, diameter, and height of each cone.
1. h = 6 mm
r = 5 mm
2. 12 m
20 m
Radius: 5 mm
Diameter: 10 mm
Height: 6 mm
3.
7 ft
10 ft 4.
4 yd
11 yd
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5. 6 m
[ 8 m ]
6.
3 ft
[ 3 ft ]
7. 8 in.
3 in.
8. 2 mm
5 mm
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Calculate the volume of each cone. Use 3.14 for π.
9.
5 cm
4 cm
The area of the base is π ? 42 5 π ? 16 < 50.24 cm2.
The volume of the cone is 1 __ 3
(50.24 ? 5) 5 1 __ 3 (251.20) < 83.73 cm3.
10.
2 cm
7 cm
11. 6 in.
3 in.
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12. 4 in.
13 in.
13.
15 m
10 m
14.
5 m
m
14 mm
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15. 5 cm
6.5 cm
16. 1 cm
3.2 cm
17.
7 ft
4.5 ft
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18.
7 ft
16.4 ft
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Lesson 9.3 Skills Practice
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All BubblyVolume of a Sphere
VocabularyDescribe the similarities and differences between each term.
1. radius of a sphere and diameter of a sphere
2. diameter of a sphere and antipodes of a sphere
3. radius of a sphere and center of a sphere
4. hemisphere and sphere
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Problem SetList the radius, diameter, distance of the center point to all other points on the sphere, and the
approximate circumference. Use 3.14 for π.
1. 2.
4 m
6 in.
Radius: 4 m
Diameter: 8 m
Center: 4 m from all points
Circumference: 8π, or about 25.12 m
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3. 4.
11 m
9 in.
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5. 6.
2.5 mm
3.25 ft
Calculate the volume of each sphere. Use 3.14 for π. Round decimals to the nearest tenth, if necessary.
7. r 5 7 m 8. r 5 6 in.
r = 7 m r = 6 in.
V 5 4 __ 3
πr3
V 5 4 __ 3
π(7)3
V 5 1372 _____ 3 π
V < 1436.0 m3
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9. d 5 20 in. 10. d 5 16 m
d = 20 in. d = 16 m
11. r 5 2.5 cm 12. r 5 11.25 mm
r = 2.5 cm r = 11.25 mm
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13. The radius of a sphere is 8 meters. 14. The radius of a sphere is 12 feet.
15. The diameter of a sphere is 20 centimeters. 16. The diameter of a sphere is 15 yards.
Calculate the volume of the sphere using the radius, diameter, or circumference given. Use 3.14 for π.
17. The Atomium in Brussels, Belgium is a model of a unit cell of an iron crystal magnified 165 billion
times. The model is made up of 8 steel spheres as vertices connected by tubes to form a cube
shape with another sphere in the center. Each sphere of the Atomium is 18 meters in diameter.
What is the volume of each sphere in the Atomium?
V 5 4 __ 3
πr3
5 4 __ 3 π(9)3
< 4 __ 3
(3.14)(729)
< 3052.08
The volume of each sphere of the Atomium is approximately 3052.08 cubic meters.
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18. Spaceship Earth is the most recognizable structure at Epcot Center at Disney World in Orlando
Florida. The ride is a geodesic sphere made up of thousands of small triangular panels. The
circumference of Spaceship Earth is 518.1 feet. What is its volume?
19. The Oriental Pearl Tower in Shanghai, China is a 468-meter high tower with 11 spheres along the
tower. Two spheres are larger than the rest and house meeting areas, an observation deck, and a
revolving restaurant. The lower of the two larger spheres has a radius of 25 meters and the higher
sphere has a radius of 22.5 meters. What is the total volume of the two largest spheres on the
Oriental Pearl Tower?
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20. The Globe Arena in Stockholm, Sweden is the world’s largest hemispherical building. The diameter
of the arena is 110 meters. The Globe Arena represents the sun in the world’s largest scale model
of the solar system. The Globe Arena is not a complete sphere, but if it were, what would its
volume be?
21. A model of Earth is located 7600 meters from the Globe Arena in Sweden’s solar system model.
The circumference of the Earth model is 56.52 centimeters. What is the volume of the Earth
model?
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22. The Montreal Biosphere is a geodesic dome that surrounds an environmental museum in
Montreal, Canada. The dome has a radius of 125 feet. The structure is only 75% of a full sphere.
What is its volume?
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Practice Makes PerfectVolume Problems
Problem SetUse the formulas for the volume of a cone, a sphere, and a cylinder to solve each problem.
1. Which paper cup can hold more and by how much: the cone or the cylinder?
1.5 in. 2 in.
3 in. 4.5 in.
V 5 πr2h V 5 1 __ 3 πr2h
5 1 __ 3 π(2)2 (4.5)
5 6π
< 18.84 in.3
5 π (1.5)2 (3)
5 6.75π
< 21.195 in.3
21.195
218.840
2.355
The cylindrical cup holds about 2.355 cubic inches more than the conical cup.
Lesson 9.4 Skills Practice
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2. Calculate the total volume of the Erlenmeyer flask.
20 cm
4 cm
20 cm
10 cm
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3. The drinking glass is not a cylinder, but is actually part of a cone. Determine the volume of
the glass.
4.5 cm
3.5 cm
16 cm
26 cm
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4. A tennis ball company is designing a new can to hold 3 tennis balls. They want to waste
as little space as possible. How much space does each can waste? Which can design
should they choose?
1.25 in.
1.25 in.
2.75 in. 5.5 in.
5.5 in.7.75 in.
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5. A candle company makes pillar candles, spherical candles, and conical candles. They have an
order for 3 pillar, 2 spherical, and 1 conical candle. Wax is sold in large rectangular blocks. What
are the possible dimensions for a wax block that could be used to fill this order?
5 in.
1.5 in.
2 in.
2.5 in.
4 in.
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6. A jeweler sold a string of fifty 8-millimeter pearls. He needs to choose a box to put them in.
Which box should the jeweler choose?
A
B25 mm
10 mm
15 mm
40 mm
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7. An ice cream shop sells cones with a volume of 94.2 cubic centimeters. They want to double the
volume of their cones without changing the diameter of the cone so the ice cream scoop will stay
on top of the cone. What should the dimensions of the new cone be if the old cone had a height of
10 centimeters?
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8. If you have a cylinder with a certain volume and you need another cylinder with the same volume
but with double the radius, how should the height of the new cylinder relate to the height of the
original cylinder? Give an example with measurements.
