3 APPLY
ASSIGNMENT GUIDE
GUIDED PRACTICE
✓
Concept Check ✓
Vocabulary Check
BASIC
?㛭㛭㛭 and volume is measured in 㛭㛭㛭㛭㛭
?㛭㛭㛭.
1. Surface area is measured in 㛭㛭㛭㛭㛭
square units; cubic units
2. Each stack of memo papers shown contains
500 sheets of paper. Explain why the stacks
have the same volume. Then calculate the
volume, given that each sheet of paper is
3 inches by 3 inches by 0.01 inches. See margin.
Day 1: pp. 746–747 Exs. 10–33
Day 2: pp. 748–749 Exs. 34–49,
51–60
AVERAGE
Day 1: pp. 746–747 Exs. 10–33
Day 2: pp. 748–749 Exs. 34–49,
51–60
ADVANCED
Day 1: pp. 746–747 Exs. 10–33
Day 2: pp. 748–749 Exs. 34–61
BLOCK SCHEDULE
pp. 746–747 Exs. 10–33
(with 12.3)
pp. 748–749 Exs. 34–49, 51–60
(with 12.5)
Skill Check
✓
2. The two stacks have
the same height and
the same crosssectional area at every
level. Therefore, by
Cavalieri’s Principle,
the two stacks have the
same volume; 45 in.3.
Use the diagram to complete the table.
l
w
h
Volume
3.
17
3
5
?
㛭㛭㛭
4.
?
㛭㛭㛭
8
10
160
5.
4.8
6.1
?
㛭㛭㛭
161.04
5.5
6.
6t
?
㛭㛭㛭
3t
54t 3
3t
EXERCISE LEVELS
Level A: Easier
10–14
Level B: More Difficult
15–49, 51–60
Level C: Most Difficult
50
h
2
FISH TANKS Find the volume of the tank.
7.
HOMEWORK CHECK
To quickly check student understanding of key concepts, go over
the following exercises: Exs. 10,
15, 16, 20, 26, 30, 32, 36, 42. See
also the Daily Homework Quiz:
• Blackline Master (Chapter 12
Resource Book, p. 67)
•
Transparency (p. 90)
255
See margin.
8.
6 in.
w
L
9.
10 in.
10 in.
15 in.
8 in.
6 in.
10 in.
14 in.
800 in.3
540π ≈ 1696 in.3
840 in.3
PRACTICE AND APPLICATIONS
STUDENT HELP
Extra Practice
to help you master
skills is on p. 826.
USING UNIT CUBES Find the number of unit cubes that will fit in the box.
Explain your reasoning.
10.
3
11.
12.
4
4
11. 100 unit cubes;
4 layers of 5 rows of
5 cubes each
6
10
120 unit cubes; 3 layers of
4 rows of 10 cubes each
5
5
2
See margin.
36 unit cubes;
6 layers of
3 rows of
2 cubes each
3
VOLUME OF A PRISM Find the volume of the right prism.
STUDENT HELP
HOMEWORK HELP
13.
14.
Example 1: Exs. 10–12
Example 2: Exs. 13–27
Example 3: Exs. 28–33
Example 4: Exs. 34–37
8 in.
3
512 in.
746
12 cm
10 in.
8 in.
8 in.
746
15.
Chapter 12 Surface Area and Volume
4 cm
5 cm
3
240 cm
3.5 in.
735兹3苶
} ≈ 318.26 in.3
4
VOLUME OF A CYLINDER Find the volume of the right cylinder. Round the
result to two decimal places.
6785.84 m3
381.00 cm3
288.40 ft3
16.
17.
18.
3 ft
7 cm
12 m
9.9 cm
10.2 ft
VISUAL THINKING Make a sketch of the solid and find its volume. Round
the result to two decimal places. 19–24. Check sketches.
240 m3
19. A prism has a square base with 4 meter sides and a height of 15 meters.
20. A pentagonal prism has a base area of 24 square feet and a height of 3 feet. 72 ft3
21. A prism has a height of 11.2 centimeters and an equilateral triangle for a
base, where each base edge measures 8 centimeters. 310.38 cm3
22. A cylinder has a radius of 4 meters and a height of 8 meters.
402.12 m3
23. A cylinder has a radius of 21.4 feet and a height of 33.7 feet. 48,484.99 ft3
24. A cylinder has a diameter of 15 inches and a height of 26 inches. 4594.58 in.3
INT
STUDENT HELP
NE
ER T
HOMEWORK HELP
Visit our Web site
www.mcdougallittell.com
for help with Exs. 25–27.
VOLUMES OF OBLIQUE SOLIDS Use Cavalieri’s Principle to find the volume
135兹3苶
of the oblique prism or cylinder.
} ≈ 116.91 cm3
2
924 m3
200π ≈ 628.32 ft3
25.
26.
27.
MATHEMATICAL REASONING
EXERCISES 16–18 Though a
cylinder doesn’t have straight
edges like a rectangular prism, its
volume is still measured in cubic
units, as is true for any solid. Have
students imagine filling a cylinder
with unit cubes. They will notice
that not all the space will be filled.
Then have them imagine filling the
cylinder with cubes with side
lengths only half of those of the unit
cubes. Point out that these cubes
will fill more of the space. By continuing to use smaller and smaller
cubes, the sum of the volumes of
the cubes will get closer and closer
to the volume of the cylinder. So, as
for a rectangular prism, the volume
of a cylinder can be thought of as
the sum of the volumes of little
cubes each with a volume given by
the three-dimensional product of its
length, width, and height.
5 ft
STUDENT HELP NOTES
15 cm
14 m
8 ft
7m
60ⴗ
11 m
6m
3 cm
3 cm
xy USING ALGEBRA Solve for the variable using the given measurements.
The prisms and the cylinders are right.
28. Volume = 560 ft3
29. Volume = 2700 yd3
u
v
8 cm
w
v
5 cm
3
3兹10
苶0苶 ≈ 13.92 yd
10 ft
31. Volume = 72.66 in.3
30. Volume = 80 cm3
v
8 ft
7 ft
Homework Help Students
can find help for Exs. 25–27 at
www.mcdougallittell.com. The
information can be printed out
for students who don’t have
access to the Internet.
32. Volume = 3000 ft3
9.3 ft
y
4 cm
33. Volume = 1696.5 m3
z
15 m
x
2 in.
1211兹3苶
} ≈ 6.99 in.
300
100,000
}} ≈ 11.04 ft
2883π
冪}莦111莦0}3莦π1 ≈ 6.00 m
12.4 Volume of Prisms and Cylinders
747
747
34.
COMMON ERROR
EXERCISE 27 Some students
may multiply the base area of the
prism by the slant height. Remind
them that the volume of an oblique
prism or cylinder is the product of
the base area and the height of the
solid, not its slant height. In this
exercise, students must use the
Pythagorean Theorem to find the
height, given the slant height.
CONCRETE BLOCK In Example 4 on page 745, find the volume of the
entire block and subtract the volume of the two rectangular prisms. How does
your answer compare with the volume found in Example 4?
The answer is the same, about 0.4 ft3.
FINDING VOLUME Find the volume of the entire solid. The prisms and
cylinders are right.
605π ≈ 1900.66 in.3
150 ft3
821.88 m3
35.
36.
37.
3 in.
8 in.
3
m
1.8
m
5 ft
2 ft
3 ft
2 ft
6 ft
9m
11 in.
10 ft
7.8 m
12.4 m
CONCRETE In Exercises 38–40, determine the number of yards of
concrete you need for the given project. To builders, a “yard” of concrete
means a cubic yard. (A cubic yard is equal to (36 in.)3, or 46,656 in.3.)
38. A driveway that is 30 feet long, 18 feet wide, and 4 inches thick 6 }2} yd
3
39. A tennis court that is 100 feet long, 50 feet wide, and 6 inches thick about 92.6 yd
40. A circular patio that has a radius of 24 feet and is 8 inches thick about 44.7 yd
41. No; the circumference of
the base of the shorter
cylinder is 11 in., so the
radius is about 1.75 in.
and the volume is
about 82 in.3. The
circumference of the
base of the taller
cylinder is 8.5 in., so the
radius is about 1.35 in.
and the volume is about
63 in.3.
41.
LOGICAL REASONING Take two sheets of
1
paper that measure 8ᎏᎏ inches by 11 inches and
2
form two cylinders; one with the height as
1
2
8ᎏᎏ inches and one with the height as 11 inches.
Do the cylinders have the same volume? Explain.
CANDLES In Exercises 42–44, you are melting a block of wax to make
candles. How many candles of the given shape can be made using a block
that measures 10 cm by 9 cm by 20 cm? The prisms and cylinder are right.
6 candles
2 candles
7 candles
42.
43.
44.
6 cm
8 cm
12 cm
ADDITIONAL PRACTICE
AND RETEACHING
For Lesson 12.4:
• Practice Levels A, B, and C
(Chapter 12 Resource Book,
p. 57)
• Reteaching with Practice
(Chapter 12 Resource Book,
p. 60)
•
See Lesson 12.4 of the
Personal Student Tutor
For more Mixed Review:
•
Search the Test and Practice
Generator for key words or
specific lessons.
748
10 cm
12 cm
45. Prism: volume = 36 in.3,
9 cm
3 cm
surface area = 66 in.2;
3
cylinder: volume ≈ 36 in. , 45.
CANNED GOODS Find the volume and surface area of a prism with a
surface area ≈ 62.2 in.2;
height
of 4 inches and a 3 inch by 3 inch square base. Compare the results
the cylinder and the prism
with the volume and surface area of a cylinder with a height of 5.1 inches
hold about the same
and a diameter of 3 inches. Use your results to explain why canned goods
amount. The cylinder has
smaller surface area, so
are usually packed in cylindrical containers.
less metal would be
needed and it would be
AQUARIUM TANK The Caribbean Coral Reef Tank
cheaper to produce a
at the New England Aquarium is a cylindrical tank
cylindrical can than one that is 23 feet deep and 40 feet in diameter, as shown.
shaped like a prism.
46. How many gallons of water are needed to fill the
23 ft
tank? (One gallon of water equals 0.1337 cubic foot.)
about 216,175 gal
47. Determine the weight of the water in the tank. (One
gallon of salt water weighs about 8.56 pounds.)
about 1,850,458 lb
748
Chapter 12 Surface Area and Volume
40 ft
Test
Preparation
48. MULTIPLE CHOICE If the volume of the
rectangular prism at the right is 1, what
does x equal? A
A
¡
D
¡
B
¡
E
¡
1
ᎏᎏ
4
4
¬
ᎏᎏ
4
C
¡
4 ASSESS
x
4
L
¬
DAILY HOMEWORK QUIZ
L
4¬
49. MULTIPLE CHOICE What is the volume of a cylinder with a radius of 6 and a
E
height of 10?
★ Challenge
A
¡
B
¡
60π
90π
C
¡
D
¡
120π
180π
E
¡
Transparency Available
1. Find the volume of the right
prism.
660 m 3
360π
50. Suppose that a 3 inch by 5 inch index card is rotated around a horizontal line
and a vertical line to produce two different solids, as shown. Which solid has
a greater volume? Explain your reasoning.
11 m
5 in.
8m
3 in.
3 in.
EXTRA CHALLENGE
5 in.
www.mcdougallittell.com
Let H be the solid produced by rotating the card around a horizontal line and V the
solid produced by rotating the card around a vertical line. V has greater volume. H has
radius 3 in. and height 5 in., so the volume of H is 45π, or about 141 in.3. V has radius
5 in. and height 3 in., so the volume of V is 75π, or about 236 in.3.
MIXED REVIEW
17 m
USING RATIOS Find the measures of the angles in the triangle whose
angles are in the given extended ratio. (Review 8.1)
51. 2:5:5
52. 1:2:3
53. 3:4:5
30°, 60°, 90°
30°, 75°, 75°
45°, 60°, 75°
FINDING AREA In Exercises 54–56, find the area of the figure. Round your
result to two decimal places. (Review 11.2, 11.5 for 12.5)
54.
55.
2. Find the volume of a right
cylinder that has a diameter
of 12 yd and a height of 11 yd.
Round the result to one decimal place. 1244.1 yd 3
3. A heptagonal prism has a
base area of 24 in.2 and a
height of 5 in. What is its
volume? 120 in.3
4. Use Cavalieri’s Principle to
find the volume of the oblique
cylinder. Leave the result in
terms of ␲.
15 cm
56.
10.12 ft
8.5 in.
7 cm
735␲ cm 3
7m
80.44 ft 2
98 m 2
5. A right rectangular prism has
a volume of 385 m 3. Its bases
have sides of length 5 m and
7 m. What is its height? 11 m
2
250.28 in.
57. SURFACE AREA OF A PRISM A right rectangular prism has a height of
13 inches, a length of 1 foot, and a width of 3 inches. Sketch the prism and
find its surface area. (Review 12.2) Check drawings; 462 in.2
SURFACE AREA Find the surface area of the solid. The cone is right and the
See margin.
pyramids are regular. (Review 12.3)
58.
59.
60.
17 ft
9 cm
12.4 ft
9114π
}} ≈ 1145.30 ft 2
25
8 in.
6 cm
144 cm 2
4 in.
96 + 24兹3苶 ≈ 137.57 in.2
12.4 Volume of Prisms and Cylinders
Additional Test Preparation Sample answer: 1.
9
7
4
749
EXTRA CHALLENGE NOTE
Challenge problems for
Lesson 12.4 are available in
blackline format in the Chapter 12
Resource Book, p. 64 and at
www.mcdougallittell.com.
ADDITIONAL TEST
PREPARATION
1. OPEN ENDED Draw a right
rectangular prism that has a
volume of 252 cubic units. Label
its length, width, and height.
See sample answer at left.
749