Date:
P
H A TE
14
R
C
Name:
Surface Area and Volume
Lesson 14.1 Building Solids Using Unit Cubes
How many unit cubes are used to build each solid?
1.
unit cubes
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2.
unit cubes
Extra Practice 5B
121
Name:
Date:
3.
unit cubes
4.
unit cubes
122
unit cubes
Chapter 14 Lesson 14.1
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5.
Name:
Date:
Lesson 14.2 Drawing Cubes and Rectangular Prisms
Draw on dot paper.
1.
Draw a unit cube.
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2.
Draw two different views of a rectangular prism made up of 2 unit cubes.
3. Draw a cube made up of 8 unit cubes.
Extra Practice 5B
123
Name:
Date:
Draw these cubes or rectangular prisms on the dot paper.
4.
5.
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6.
124
Chapter 14 Lesson 14.2
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Name:
7.
Date:
8.
9.
Extra Practice 5B
125
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Name:
126
Chapter 14 Lesson 14.2
Date:
10.
11.
12.
Name:
Date:
Complete the drawing of each cube or rectangular prism.
13.
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14.
Extra Practice 5B
127
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Name:
128
Chapter 14 Lesson 14.2
Date:
15.
16.
Name:
Date:
Lesson 14.3
Prisms and Pyramids
Theflatsurfaceofasolid
iscalledaface.
Twofacesmeetatanedge.
Edgesmeetatavertex.
Themathematicalname
forcornersisvertices.
Complete the table.
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Solid
1.
Cube
2.
Rectangular
prism
3.
Triangular
prism
4.
Square
pyramid
5.
Triangular
pyramid
Number of
Faces (F)
Number of
Vertices (V)
Number of
Edges (E)
Extra Practice 5B
129
Name:
Date:
Complete.
6.
What general statement can you make about the number of faces, the
number of vertices, and the number of edges of prisms and pyramids?
Classify the following objects and write your answer in the table provided.
A
B
C
D
E
F
Prisms
130
Chapter 14 Lesson 14.3
Pyramids
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7.
Name:
Date:
Lesson 14.4 Nets and Surface Area
Find the surface area.
1.
The diagram shows the net of a cube.
Find the surface area of the cube.
4cm
4cm
4cm
2.
The diagram shows the net of a rectangular prism.
Find the surface area of the rectangular prism.
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5cm
3cm
2cm
Extra Practice 5B
131
Name:
Date:
The diagrams show the nets of cubes or rectangular prisms.
Find the surface area of each cube or rectangular prism.
3.
5cm
4.
10cm
6cm
20cm
5.
10cm
18cm
132
Chapter 14 Lesson 14.4
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6cm
Name:
Date:
Which of these nets can be folded to form a cube?
Shade the circles that represent the correct answers.
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6.
Extra Practice 5B
133
Name:
Date:
Which of these nets can be folded to form a rectangular prism?
Shade the circles that represent the correct answers.
8.
Which of these nets can be folded to form a triangular prism?
Shade the circles that represent the correct answers.
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7.
134
Chapter 14 Lesson 14.4
Name:
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9.
Date:
Which of these nets can be folded to form a square pyramid?
Shade the circles that represent the correct answers.
Extra Practice 5B
135
Name:
Date:
Which of the nets can be folded to form a triangular pyramid? Shade the
circles that represent the correct answers.
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10.
136
Chapter 14 Lesson 14.5
Name:
Date:
Lesson 14.5 Understanding and Measuring Volume
These solids are formed by stacking unit cubes in the corner of a room.
Find the volume of each solid.
1.
Solid A
Volume 5
cubic units
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2.
Solid B
Volume 5
cubic units
Extra Practice 5B
137
Name:
Date:
3.
Solid C
Volume 5
cubic units
Solid D
Volume 5
cubic units
Compare the volumes of the solids in Exercises 1 to 4.
Then fill in the blanks.
5.
Solid
has the least volume.
6.
Solid
and Solid
138
Chapter 14 Lesson 14.5
have the same volume.
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4.
Name:
Date:
These solids are formed by stacking unit cubes in the corner of a room.
Find the volume of each solid.
7.
Solid E
Volume 5
cubic units
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8.
Solid F
Volume 5
cubic units
Extra Practice 5B
139
Name:
Date:
9.
Solid G
Volume 5
cubic units
Solid H
140
Volume 5
Chapter 14 Lesson 14.5
cubic units
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10.
Name:
Date:
Compare the volumes of the solids in Exercises 7 to 10.
Then fill in the blanks.
11.
Solid
has the least volume.
12.
Solid
has the greatest volume.
13.
Solid
and Solid
have the same volume.
These solids are built using 1-centimeter cubes.
Find the volume of each solid. Then fill in the blanks.
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14.
15.
Length 5
cm
Length 5
cm
Width 5
cm
Width 5
cm
Height 5
cm
Height 5
cm
Volume 5
cm3
Volume 5
cm3
Extra Practice 5B
141
Name:
Date:
16.
Length 5
cm
Width 5
cm
Height 5
cm
Volume 5
cm3
Length 5
cm
Width 5
cm
Height 5
cm
Volume 5
cm3
142
Chapter 14 Lesson 14.5
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17.
Name:
Date:
Lesson 14.6 Volume of a Rectangular Prism
and Liquid
Find the volume of each rectangular prism.
1.
7cm
8cm
5cm
Length 5
cm
Width 5
cm
Height 5
cm
Volume 5
3
cm3
5
3
2.
10cm
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7cm
14cm
Length 5
cm
Width 5
cm
Height 5
cm
Volume 5
3
cm3
5
3
Extra Practice 5B
143
Name:
Date:
Find the volume of each rectangular prism.
3.
20cm
28cm
32cm
Length 5
cm
Width 5
cm
Height 5
cm
Volume 5
3
cm3
5
3
18cm
12cm
25cm
Volume 5
3
cm3
144
5
Chapter 14 Lesson 14.6
3
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4.
Name:
Date:
5.
28cm
15cm
15cm
Volume 5
3
cm3
5
3
Find the length of the unknown edge of each rectangular prism.
6.
15cm
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6cm
720cm3
Width 5
?
cm
7.
? 648cm3
6cm
Height 5
9cm
cm
Extra Practice 5B
145
Name:
Date:
8.
7cm
756cm3
6cm
?
Length 5
9.
The figure is a rectangular prism with a square base.
cm
13cm
832cm3
?
Length 5
cm
Write each measure in cubic centimeters.
390 mL 5
12.
2 L 600 mL 5
14.
5 L 50 mL 5
cm3
11.
cm3 13.
cm3
15.
1 L 125 mL 5
4 L 80 mL 5
2 L 6 mL 5
Write each measure in liters and milliliters or liters.
16.
890 cm3 5
17.
1,850 cm3 5
L
mL
18.
3,065 cm3 5
L
mL
146
Chapter 14 Lesson 14.6
L
mL
cm3
cm3
cm3
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10.
Name:
19.
530 cm3 5
21.
1,650 cm3 5
L
L
Date:
20.
755 cm3 5
22.
2,075 cm3 5
L
L
Find the volume of water in each rectangular tank in milliliters.
(Hint: 1 cm3 5 1 mL)
23.
24.
15cm
16cm
12cm
18cm
26cm
32cm
Volume 5
Volume 5
Find the volume of water in each rectangular tank in liters.
(Hint: 1 cm3 5 1 mL; 1,000 cm3 5 1 L)
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25.
26.
15cm
12cm
28cm
18cm
15cm
20cm
Volume 5
Volume 5
Extra Practice 5B
147
Name:
Date:
Solve. Show your work.
27.
A rectangular fish tank measures 38 centimeters by 23 centimeters by
18 centimeters. How much water is in the tank when it is _
​ 23 ​-full? Give your
answer in liters and milliliters.
18cm
38cm
23cm
28.
A rectangular tank measuring 30 centimeters long, 22 centimeters wide,
​ 14 ​of the water is removed, what
and 25 centimeters high is _
​ 45 ​-full of water. If _
is the volume of water left in the tank? Give your answer in liters.
25cm
29.
A rectangular tank measuring 42 centimeters by 20 centimeters by
24 centimeters is filled with water to a height of 7 centimeters. What is the
volume of water needed to fill the tank completely? Give your answer in liters.
24cm
7cm
42cm
148
Chapter 14 Lesson 14.6
20cm
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30cm
22cm
Name:
Date:
Find the volume of each cube or rectangular prism.
30.
31.
7in.
10cm
7in.
10cm
7in.
10cm
32.
33.
10in.
6in.
9in.
20cm
10cm
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15cm
34.
8in.
35.
12in.
6in.
12cm
20cm
12cm
Extra Practice 5B
149
Name:
Date:
36.
The length of a cube is 9 centimeters. Find the volume of the cube.
37.
A rectangular piece of wood has a length of 30 centimeters and a square
base with sides that measure 6 centimeters. What is the volume of the piece
of wood?
38.
An open rectangular water tank measures 20 inches by 18 inches by
16 inches. Find the volume of the tank.
16in.
18in.
20in.
150
Chapter 14 Lesson 14.6
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Solve. Show your work.
Name:
Date:
Lesson 14.7 Volume of Composite Solids
Solve. Show your work.
1.
This solid is made up of two rectangular prisms. Find the volume of the solid.
6 cm
5 cm
6 cm
8 cm
8 cm
20 cm
Find the volume of each solid.
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2.
5 cm
5 cm
6 cm
16 cm
6 cm
18 cm
15 cm
Extra Practice 5B
151
Name:
3.
4 cm
Date:
5 cm
6 cm
5 cm 6 cm
6 cm
5 cm
6 cm
4 cm
5 cm
4.
10 in.
5 in.
16 in.
9 in.
152
Chapter 14 Lesson 14.7
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12 in.
Name:
5.
Date:
10 in.
8 in.
8 in.
10 in.
8 in.
30 in.
10 in.
20 in.
6.
6 cm
1
_
2 2 cm
1
_
2 2 cm
6 cm
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6 cm
6 cm
1
_
2 2 cm
30 cm
6 cm
1
_
7 2 cm
Extra Practice 5B
153
Name:
7.
Date:
A small block of wood was cut out from a piece of rectangular block of
wood measuring 24 inches by 10 inches by 14 inches. Find the volume of the
remaining piece of wood.
14 in.
8 in.
8 in.
12 in.
10 in.
24 in.
The following figure shows the arch-way of a playground. Find the volume of
material which is used to build the arch-way.
3 ft
2
_
6 3 ft
3 ft
154
Chapter 14 Lesson 14.7
12 ft
3 ft
2
_
6 3 ft
3 ft
3 ft
2
_
5 5 ft
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8.
Name:
Date:
Put on Your Thinking Cap!
Solve. Show your work.
1.
Jessica used 35 unit cubes to build the solid shown. Another row of cubes is
to be placed below the bottom row following the same pattern. How many
more cubes will Jessica need?
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Extra Practice 5B
155
Name:
2.
Paul uses 5 unit cubes to build the first figure and 8 unit cubes to build the
second figure into the T-shaped patterns shown.
Pattern1
Pattern2
a.Paul continues to build the third and fourth patterns. Find the number of
unit cubes in Patterns 3 and 4. Record your answers in the table.
T-Shaped Pattern
1
2
Number of Unit Cubes
5
51358
3
b. How many cubes would be used to build Patterns 5 and 6?
c. Find the number of unit cubes in Pattern 10.
156
Chapter 14 Put on Your Thinking Cap!
4
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Date:
Name:
3.
Date:
The solid is made up of identical cubes glued together. The surface area of
the solid is painted blue. The volume of the solid is 960 cubic centimeters.
Find the surface area that is painted blue.
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4.
In order to fill the box completely, 126 3-centimeter cubes are needed.
What is the height of the box?
?
3cm
3cm
3cm
9cm
18cm
Extra Practice 5B
157
Name:
5.
The solid is made up of 3-centimeter cubes.
a. Find the volume of the solid.
Date:
b. Find the surface area of the solid.
c. The whole solid is painted red.
i. ii. Find the number of cubes that have only three faces painted red.
158
iii. Find the number of cubes that have only four faces painted red.
Chapter 14 Put on Your Thinking Cap!
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Find the number of cubes that have only two faces painted red.
Name:
Date:
6.
Two wooden blocks, A and B, are glued together. The ratio of the volume of
block A to the volume of block B is 3 : 7.
a. What is the volume of block B?
B
12cm
6cm
b. What is the width of block B?
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?
A
10cm
Extra Practice 5B
159
Name:
Date:
7.
A cubic container was completely filled with water. When _
​ 34 ​of the water
from the container was poured into a rectangular tank, the tank became
1
​ _
4 ​full. The capacity of the tank is 1,024 liters more than that of the cubic
container. Find the length of the cubic container.
waterispoured
intothetank
Container
Tank
8.
John wanted to build a model wall measuring 36 centimeters long,
8 centimeters wide, and 21 centimeters high. He used blocks that measured
3 centimeters by 4 centimeters by 2 centimeters. John stopped after
building _
​ 59 ​of the wall. How many more blocks will John need to complete
the wall?
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160
Chapter 14 Put on Your Thinking Cap!
Name:
9.
Date:
How many 2-centimeter cubes can be packed into a rectangular prism
measuring 25 centimeters by 15 centimeters by 20 centimeters?
20cm
2cm
2cm
2cm
10.
Cube
15cm
25cm
Prism
Identical watch boxes each measuring 10 centimeters by 8 centimeters by
6 centimeters are packed in a rectangular container measuring 54 centimeters
by 44 centimeters by 22 centimeters. What is the maximum number of watch
boxes that can be packed into the container?
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22cm
10cm
Box
6cm
8cm
44cm
54cm
Container
Extra Practice 5B
161
Name:
Date:
11.
Two identical rectangular cards measuring 20 centimeters by 12 centimeters
are folded to form two different rectangular solids. Each fold was made so
height and width are equal.
a. One of the solids is shown below. Label its width and height.
b. Draw the other rectangular solid. Label its length, width, and height.
c. Find the volume of each rectangular solid.
162
Chapter 14 Put on Your Thinking Cap!
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12cm