iv. volume and volume formulas - weebly
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90 • MODULE 2: Investigating Proportionality
© C
arne
gie
Lear
ning
, Inc
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Topic 3
CIRCLES AND VOLUME
IV. Volume and Volume Formulas
A. Connect the corresponding vertices of the fi gure and the translated fi gure. Name the shape that was translated and name the resulting solid fi gure.
1.
2.
3.
4.
5.
6.
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CIRCLES AND VOLUME: Skills Practice • 91
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Name Date
Topic 3
CIRCLES AND VOLUME
B. Name the solid formed by stacking 1000 of the congruent shapes shown.
C. Name the solid formed by stacking similar shapes so that each layer of the stack is composed of a slightly smaller shape than the previous layer.
1. 2.
3. 4.
5. 6.
1. 2.
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92 • MODULE 2: Investigating Proportionality
© C
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Topic 3
CIRCLES AND VOLUME
3. 4.
1. 2.
5. 6.
3. 4.
5. 6.
D. Calculate the volume of each cylinder. Use 3.14 for p. Round decimals to the nearest tenth, if necessary.
7 m
30 yd
22 yd
20 m
5 m
10 ft
4.5 ft
4 mm
6 mm
16 ft
5 ft
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CIRCLES AND VOLUME: Skills Practice • 93
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Name Date
Topic 3
CIRCLES AND VOLUME
1. 2.
3. 4.
7. 8.
5. 6.
E. Calculate the volume of each cone. Use 3.14 for p. Round answers to the nearest hundredth, if necessary.
5 cm
4 cm
7 cm2 cm
6 in.
3 in.
4 in.13 in.
10 m
15 m 14 mm
5 m
m
9 m
12 m
3.5 cm
13 cm
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94 • MODULE 2: Investigating Proportionality
© C
arne
gie
Lear
ning
, Inc
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Topic 3
CIRCLES AND VOLUME
7. 8.
5 cm
6.5 cm
1 cm
3.2 cm
1. 2.
10 in.10 in.
9 in.
12 ft12 ft
9 ft
3. 4.
11 cm
7 cm7 cm 25 m
25 m
20 m
F. Calculate the volume of each square pyramid. Round answers to the nearest hundredth, if necessary.
5. 6.
30 ft30 ft
22 ft
28 mm
21 mm21 mm
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CIRCLES AND VOLUME: Skills Practice • 95
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Name Date
Topic 3
CIRCLES AND VOLUME
7. 8.
42 in.42 in.
34.5 in.
90 cm90 cm
75 cm
1. r 5 7 meters 2. r 5 6 inches
r
G. Calculate the volume of each sphere. Use 3.14 for p. Round decimals to the nearest tenth, if necessary.
r
3. d 5 20 inches 4. d 5 16 meters
d d
5. r 5 2.5 centimeters 6. r 5 11.25 millimeters
r r
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96 • MODULE 2: Investigating Proportionality
© C
arne
gie
Lear
ning
, Inc
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Topic 3
CIRCLES AND VOLUME
V. Surface Area
A. Determine the total surface area of each right prism. Bases with a single label on one edge are regular polygons. Round your answer to the nearest hundredth, where appropriate.
B. Determine the total surface area of each right pyramid. Bases with a single label on one edge are regular polygons. All other bases are rectangles. Round your answer to the nearest hundredth, where appropriate.
1.
4
73
2.
5
134
1.
8 in.6 in.
7 in.
2.
12 cm9 cm
15 cm
3.
6 in.
8 in.9 in.
4.
12 cm10 cm
16 cm
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CIRCLES AND VOLUME: Skills Practice • 97
© C
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Lear
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Name Date
Topic 3
CIRCLES AND VOLUME
C. Determine the total surface area of each right cylinder. Round your answer to the nearest hundredth.
1.
5 cm
8 cm
2.
9 cm
23 cm
3.
7.5 cm
6 cm
4.
86 m
35 m
3.
7 m
8 m
4.
4 mm
10 mm
15 mm
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98 • MODULE 2: Investigating Proportionality
© C
arne
gie
Lear
ning
, Inc
.
Topic 3
CIRCLES AND VOLUME
D. Determine the total surface area of each right cone. Round your answer to the nearest hundredth.
E. Determine the total surface area of each sphere. Round your answer to the nearest hundredth.
1.
12 ft
5 ft
2.
15 cm
12 cm
1.
r = 7.5 cm
2.
r = 6 cm
3.
14 in.
18 in.
4.
21 cm
18 cm
3.
d = 22 in.
4.
d = 4 cm
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