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Volume of a Prism
BEFORE
Now
WHY?
You found the surface area of
a rectangular prism.
You’ll find the volume of a
rectangular prism.
So you can find the length of a pool
at an aquarium, as in Example 3.
In the Real World
Word Watch
volume, p. 510
Block Puzzles A manufacturer puts
puzzles into cube-shaped boxes.
Groups of the boxes are stacked, as
shown in Example 1, and then put into
a rectangular carton for shipping. How
many puzzle boxes will fit in one carton?
EXAMPLE
1
Counting Cubes in a Stack
To find the total number of puzzle boxes
that will fit in one carton, multiply the number
of boxes in one layer by the number of layers.
The boxes are stacked in 2 layers. Each layer
is a rectangle that is 4 boxes long and 3
boxes wide.
2
4
3
Boxes in one layer Number of layers Number of boxes
3 4 2 24
ANSWER The manufacturer can fit 24 puzzle boxes in one carton.
The volume of a solid, such as the box in Example 1, is the amount of
space the solid occupies. Volume is measured in cubic units. One way to
find the volume of a rectangular prism is to use the formula below.
Volume of a Rectangular Prism
Words Volume length p width p height
Algebra
h
V lwh
l
w
510
Chapter 10
Geometry and Measurement
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EXAMPLE
2
Finding the Volume of a Prism
Find the volume of the rectangular prism.
4 in.
V lwh
Write the volume formula.
8p6p4
8 in.
Substitute for l, w, and h.
6 in.
192
Simplify.
ANSWER The volume is 192 cubic inches.
Your turn now
Find the volume of the rectangular prism.
1.
2.
3.
5 in.
12 ft
4m
16 in.
20 in.
5m
EXAMPLE
3
2m
6 ft
6 ft
Using the Formula for Volume
Aquariums A pool at an aquarium is a rectangular prism that is
30 meters wide and 12 meters deep. The volume of the pool is
21,600 cubic meters. How long is the pool?
Solution
V lwh
Write the volume formula.
21,600 l p 30 p 12
Substitute for V, w, and h.
21,600 l p 360
Simplify.
l 21,600 360
Write a related division equation.
l 60
Simplify.
ANSWER The length of the pool is 60 meters.
Sea Lion at Magic Mountain
Your turn now
prisms.
In Exercises 4 and 5, the solids are rectangular
4. The volume of a swimming pool is 3750 cubic meters. The pool is
25 meters wide and 3 meters deep. How long is the pool?
5. The volume of a bathtub is 16 cubic feet. The bathtub is 4 feet long
and 2 feet wide. How deep is the bathtub?
Lesson 10.7
Volume of a Prism
511
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 717
Getting Ready to Practice
1. Vocabulary To find the _?_ of a rectangular prism, you find the product
of the length, the width, and the height.
Find the volume of the rectangular prism.
2.
3.
4.
3 cm
5m
2 ft
7 cm
25 m
6 ft
5 cm
6m
3 ft
5. Guided Problem Solving Use the pasta box
shown to find the volume of the part of the
pasta box that is not filled with pasta.
MACARONI
1 Find the volume of the pasta
box shown.
Pasta
16 cm
2 Find the volume of the pasta in the
pasta box.
7 cm
5 cm
3 Subtract the volume of the pasta from
the volume of the pasta box.
13 cm
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
6–10
6–10
11–13
Find the volume of the rectangular prism.
6.
7.
8.
12 in.
20 cm
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
13 in.
20 cm
8 in.
3 in.
20 cm
17 in.
31 in.
9. Find the volume of a rectangular prism that is 12 feet by 5 feet by 7 feet.
10. Planters A planter in the shape of a rectangular prism is 24 inches by
4 inches by 5 inches. How much dirt is needed to fill the planter?
Find the missing dimension of the rectangular prism described.
11. Volume: 60 ft 3
length: 10 ft
width: 2 ft
512
Chapter 10
Geometry and Measurement
12. Volume: 96 cm3
length: 16 cm
height: 3 cm
13. Volume: 2500 m3
width: 25 m
height: 5 m
Page 4 of 4
Sports
Extended Problem Solving In Exercises 14–16, use this information.
A gymnastics center wants to buy foam cubes for a landing pit. The landing
pit is a rectangular prism that is 120 inches long by 96 inches wide. The
volume is 829,440 cubic inches.
14. Find the depth of the landing pit.
15. Estimate Each foam cube has a side length of 6 inches. About how
many foam cubes will fit in the landing pit?
16. A company recommends buying only enough cubes to fill 70% of the
landing pit. About how many cubes should the center order?
17. Critical Thinking You find the volume of a rectangular prism using the
formula V lwh. Your friend finds the volume of the same prism by
multiplying the area of the base by the height. Are the methods the
same or are they different? Explain.
18. Writing Explain why the formula V s 3 can be used to find
the volume of a cube with a side length of s.
■
Landing Pits
Some landing pits have a
trampoline bed placed about
halfway down the pit in order
to reduce the number of
foam cubes needed.
Use the information for
Exercise 15 to estimate how
many foam cubes are needed
if a trampoline bed is placed
so that the depth of the
landing pit is 4 feet.
19. Challenge Find all the different whole number lengths, widths,
and heights a rectangular prism can have if its volume is
375 cubic centimeters.
Mixed Review
20. Your time in a road race is 40 minutes and 32 seconds. Your friend
finishes 3 minutes and 43 seconds later. What is your friend’s time?
(Lesson 6.6)
21. Find the surface area of a rectangular prism that is 22 centimeters by
4 centimeters by 15 centimeters. (Lesson 10.6)
Basic Skills Copy and complete the statement with <, >, or .
7
3
22. _?_ 10
10
1
7
23. _?_ 8
8
5
4
24. _?_ 12
9
2
10
25. _?_ 3
15
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
26. Multiple Choice What is the volume of a rectangular prism that is
18 meters by 15 meters by 12 meters?
A. 45 m3
B. 90 m3
C. 1332 m3
D. 3240 m3
27. Multiple Choice The volume of a fish tank is 864 cubic inches. The fish
tank is a rectangular prism. The length of the fish tank is 12 inches and
the height is 9 inches. What is the width of the fish tank?
F. 4 inches
G. 8 inches
H. 648 inches
Lesson 10.7
I. 843 inches
Volume of a Prism
513