Name Class 8-6
Date Volume of Prisms
Going Deeper
Essential question: How do you find the volume of a rectangular prism?
CC.6.G.2
1
EXPLORE
video tutor
Volume of a Prism
A cube with edge length 1 unit and volume 1 cubic unit
is filled with smaller cubes as shown.
A
How many small cubes are there?
How does the combined volume of the small cubes
compare to the volume of the large cube?
1 unit
Number of
small cubes
Volume of one
small cube
=
·
?
=
Volume of
large cube
What is the volume of one small cube?
B
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·
Each edge of the large cube contains
Number of small
cubes per edge
cubic unit(s)
small cubes.
·
Edge length of
one small cube
=
·
?
=
What is the edge length of one small cube?
C
unit(s)
Combine your results from A and B to complete the following sentence.
Each small cube has edge length
D
Edge length of
large cube
unit(s) and volume
cubic unit(s).
Remember that the formula for volume of a cube with edge length ℓ is
V = ℓ · ℓ · ℓ, or V = ℓ​ 3​ ​.
Show how to find the volume of one small cube using this formula.
V=
Chapter 8
=
371
Lesson 6
E
Several of the small cubes are arranged into a medium-sized cube
as shown.
Show two different ways to find the volume of the medium-sized cube.
Volume of a Rectangular Prism
V = ℓwh, or V = Bh
(where B represents the area of
the prism’s base; B = ℓw.)
h
w
CC.6.G.2
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EXAMPLE
Finding Volume
Find the volume of the rectangular prism.
ℓ = meters
w=
h=
meters
meters
4
=
·
·
=
·
·
=
=
Write each mixed number as
an improper fraction.
3m
2
1
m
4
Multiply.
cubic meters
Write as a mixed number in simplest form.
REFLECT
2a. Show how to use the formula V = Bh to find the volume.
Chapter 8
372
Lesson 6
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V = ℓ wh
1
m
2
TRY THIS!
Find the volume of each rectangular prism.
2b.
1
2 inches
2
4 inches
7
width = 3​ __12 ​inches
height = 3 inches
V=
1
inches
2
V=
2c. length = 5​ __41 ​inches
cubic inches
cubic inches
CC.6.G.2
3
EXAMPLE
Problem-Solving by Finding Volume
A rectangular city swimming pool is 25 meters
1 ​ meters wide, and has an average depth
long, 17​ __
2
1 ​ meters. What is the volume of the pool?
of 1​ __
2
Label the rectangular prism to represent the pool.
ℓ = meters
w=
h=
meters
meters
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V = ℓwh
=
·
·
=
·
·
=
Write each mixed number as an
improper fraction.
Multiply.
=
cubic meters
Write as a mixed number in simplest form.
TRY THIS!
3a. Miguel has a turtle aquarium that measures 18​ __12 ​inches by 12​ __12 ​inches
by 4 inches. What is the volume of the aquarium?
V=
cubic inches
REFLECT
3b. How can you use estimation to check the reasonableness of your answer
to 3a?
Chapter 8
373
Lesson 6
pra c t i c e
Find the volume of each rectangular prism.
1.
2.
5m
8m
3m
4m
10 m
V=
9m
cubic meters
3.
V=
cubic meters
4.
2 cm
2
1
4 cm
4
V=
8
3
cm
4
6m
8
cubic centimeters
5.
3
m
8
V=
cubic meters
6.
7.5 ft
8
6
9.25 ft
V=
1
in.
2
1
in.
2
12 in.
cubic feet
V=
cubic inches
7. A block of wood measures 4.5 centimeters by 3.5 centimeters by 7 centimeters.
What is the volume of the block of wood?
V=
cubic centimeters
36 in.
8. A restaurant buys a freezer in the shape of a
rectangular prism. The dimensions of the freezer
are shown. What is the volume of the freezer?
V=
cubic inches
24 in.
72 in.
9. Conjecture The length, width, and height of a rectangular prism are doubled. How many
times greater is the volume compared to the original prism?
Chapter 8
374
Lesson 6
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4 ft
1
m
4
Name Class 8-6
Date Name ________________________________________ Date __________________ Class __________________
Measurement
and Geometry
Additional
Practice
Chapter
Practice B: Volume of Prisms
Find the volume of each rectangular prism.
1.
2.
________________________
4.
3.
_______________________
5.
________________________
________________________
6.
_______________________
________________________
7. Tim made a toy chest for his little sister’s square building blocks. If 6 layers of
blocks can fit in the box, and each layer has 15 blocks, how many building blocks
can the toy chest hold in all?
© Houghton Mifflin Harcourt Publishing Company
_________________________________________________________________________________________
8. A rectangular prism’s base is 8 feet long. It is 2 1 times taller than it is long
2
1
and
as wide as it is tall. What is the volume of that prism?
2
_________________________________________________________________________________________
9. Fawn built a sandbox that is 6 feet long, 5 feet wide, and 1 foot
2
tall. How many cubic feet of sand does she need to fill the box?
_________________________________________________________________________________________
10. Unfinished lumber is sold in units called board feet. A board foot
is the volume of lumber contained in a board 1 inch thick, 1 foot
wide, and 1 foot long. How many cubic inches of wood are in
1 board foot?
_________________________________________________________________________________________
Chapter 8
375
Practice and Problem Solving
54
Holt McDougal Mathematics
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Name ________________________________________ Date __________________ Class __________________
Measurement
and Geometry
Problem
Solving
Chapter
Problem Solving: Volume of Prisms
Write the correct answer.
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?
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?
________________________________________
________________________________________
________________________________________
________________________________________
3. Nikita built a dollhouse in the shape
of a rectangular prism. The base
of the dollhouse has an area of
12 square feet. If the volume of the
dollhouse is 48 ft3, what is the height
of the dollhouse?
4. 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?
________________________________________
________________________________________
________________________________________
________________________________________
5. 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.
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
C 17.5 in.
G 14 ft3
D 9.5 in.
H 36 ft3
J 72 ft3
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Chapter 8
54
376
Practice
Problem
Solving
Holtand
McDougal
Mathematics
© Houghton Mifflin Harcourt Publishing Company
Circle the letter of the correct answer.