MSM07G6_RESBK_Ch10_053-060.pe
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Name
Date
Class
Reteach
LESSON
10-7 Volume of Prisms
Volume is the number of cubic units needed to fill a space. To find
the volume of a rectangular prism, first find the area of the base.
length ! 3 units
width ! 2 units
A ! !w ! 3 • 2 ! 6 square units.
The area of the base tells you how many cubic units are in the first
layer of the prism.
Next, multiply the result by the number of layers in the prism.
The prism has 4 layers, so multiply 6 by 4.
6 • 4 ! 24
So, the volume of the rectangular prism is 24 cubic units.
Find the volume of each rectangular prism.
1.
2.
16 suare units
30 suare units
To find the area of a triangular prism, first find the area of the base.
1
A ! !2! bh
4
1
! !2! (5 • 4)
3
! 10 square units
5
Then multiply the result by the height of the prism.
10 • 3 ! 30
The volume of the triangular prism is 30 cubic units.
Find the volume of each triangular prism.
3.
4.
2
2
4
4
16 suare units
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5
3
15 suare units
56
Holt Mathematics
Reteach
LESSON
10-7 Volume of Prisms
Practice C
LESSON
10-7 Volume of Prisms
Volume is the number of cubic units needed to fill a space. To find
the volume of a rectangular prism, first find the area of the base.
Find the volume of each rectangular prism.
1.
2.
3.
4m
1
s ! 6_2 in.
6m
5
274!8! in3
1
2_
2 ft
0.02
length ! 3 units
width ! 2 units
1
1
4_
4 ft
9_
4 ft
A ! !w ! 3 • 2 ! 6 square units.
The area of the base tells you how many cubic units are in the first
layer of the prism.
9
98!32! ft3
0.48 m3
Next, multiply the result by the number of layers in the prism.
The prism has 4 layers, so multiply 6 by 4.
Find the volume of each triangular prism.
4.
5.
10.25 cm
16.2 cm
6 • 4 ! 24
6.
1
4_
2 ft
13.7 cm
So, the volume of the rectangular prism is 24 cubic units.
1.3 m
1
2_
8 ft
3
3_
4 ft
0.7 m
119
! ft3
17!
128
1,137.4425 cm3
Find the volume of each rectangular prism.
0.05 m
1.
0.02275 m3
16 square units
Find the missing measurement for each rectangular prism.
7. !! ? ; w ! 34 m; h ! 5 m; V ! 340 m3
2m
8. ! ! 4.5 ft; w ! ? ; h ! 6 ft; V ! 256.5 ft3
9.5 ft
9. ! ! 14 yd; w ! 8 yd; h ! ? ; V ! 1,344 yd3
12 yd
1
1
2.
1
10. ! ! ? ; w ! 1!2! in.; h ! 3!2! in.; V ! 52!2! in3
1
12. A rectangular box is 3 feet wide, 6 feet long, and 4 feet tall.
Inside the box, Phil placed a triangular prism that is 3 feet tall,
and has a base 2 feet wide with a height of 5 feet. If he places
another triangular prism of the same size in the box, how
much empty space will there be in the box?
1
3
! !2! (5 • 4)
! 10 square units
5
Then multiply the result by the height of the prism.
10 • 3 ! 30
1,600 ft3
of that prism?
A ! !2! bh
4
10 in.
1
11. A rectangular prism’s base is 8 feet long. It is 2!2! times taller
1
than it is long and !2! as wide as it is tall. What is the volume
30 square units
To find the area of a triangular prism, first find the area of the base.
The volume of the triangular prism is 30 cubic units.
Find the volume of each triangular prism.
3.
4.
2
42 ft3
2
4
4
16 square units
55
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Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
15 square units
56
Did you know that most fish grow according to the size of their
tank? In fact, a freshwater fish needs about 1 gallon of water for
every inch of its body. The volume of 1 gallon of water is about
231 in3. So, a fish tank with a volume of a 700 in3 will hold
700 " 231 ! 3 gallons of water. This size tank would be the
healthiest home for a 3-inch-long fish.
Write the correct answer.
2. The Vietnam Veterans Memorial in
Washington, D.C., is a 493.5-footlong wall made of polished black
granite engraved with the names of
soldiers who died in the war. The wall
is 0.25 feet thick and has an average
height of 9 feet. About how many
cubic feet of black granite was used
in the Vietnam Veterans Memorial?
1. At 726 feet tall, Hoover Dam is one
of the world’s largest concrete dams.
In fact, it holds enough concrete to
pave a two-lane highway from New
York City to San Francisco! The dam
is shaped like a rectangular prism
with a base 1,224 feet long and
660 feet wide. About how much
concrete forms Hoover Dam?
Find the volume of each fish tank. Then match each fish to the
best tank for it.
about 586,491,840 ft3 of
Koi Goldfish
! !24 in.
Redtail Shark
! ! 5 in.
! ! 24 in.
w ! 12 in.
h ! 20 in.
Volume of Tank:
5,760 in3
Fish:
about 25
Fish:
Fish:
about 13
Volume of Tank:
about 5
Gallons of Water:
redtail shark
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1.56 cm3 of benitoite
! ! 25 in.
w ! 8 in.
h ! 8 in.
1,170 in3
Gallons of Water:
Fish:
57
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4. The Flatiron Building in New York
City is a triangular prism. A solid
bronze souvenir model of the
building is 5 inches tall, with a base
height of 1.5 inches and a base width
of 2.5 inches. How much bronze was
used to make the model?
9.375 in3 of bronze
Circle the letter of the correct answer.
clown loach
! ! 13 in.
w ! 10 in.
h ! 9 in.
granite
3. Benitoite, a triangular prism crystal,
is the official state gem of California.
One benitoite crystal found in
California is 1.2 cm tall, with a base
width of 2 cm and a base height of
1.3 cm. How many cubic centimeters
of benitoite are in that crystal?
2,970 in3
Gallons of Water:
koi goldfish
Volume of Tank:
Clown Loach
! ! 12 in.
Volume of Tank:
about 1,110.375 ft3 of black
concrete
! ! 18 in.
w ! 15 in.
h ! 11 in.
Gallons of Water:
Holt Mathematics
Problem Solving
LESSON
10-7 Volume of Prisms
Challenge
LESSON
10-7 Fish Tank Math
Angelfish
! ! 6 in.
5
3
1,600 in3
about 7
angelfish
Holt Mathematics
5. Individual slices of pizza are sold in
2-inch-tall triangular prism boxes.
The box base is 8 inches wide, with
a 7-inch height. How many cubic
inches of pizza will fit in each box?
A 112 in3
C 60 in3
B 102 in3
D 56 in3
!
6. The world’s largest chocolate bar is
a huge rectangular prism weighing
more than a ton! The bar is 9 feet long,
4 feet tall, and 1 foot wide. How many
cubic feet of chocolate does it have?
F 13 ft3
H 36 ft3
!
G 14 ft3
J 72 ft3
7. A box can hold 175 cubic inches of
cereal. If the box is 7 inches long and
2.5 inches wide, how tall is it?
A 25 in.
B 10 in.
!
C 17.5 in.
D 9.5 in.
8. A triangular prism used to reflect light
is made of 120 cm3 of glass. If the
prism is 5 centimeters tall, what is the
area of each of its triangular bases?
F 24 cm
G 12 cm
H 12 cm2
J 24 cm2
!
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90
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Holt Mathematics