3 APPLY
PRACTICE AND APPLICATIONS
STUDENT HELP
ASSIGNMENT GUIDE
BASIC
Day 1: pp. 732–734 Exs. 18–42
even, 45–47, 50–60
Extra Practice
to help you master
skills is on p. 825.
13. Give the mathematical name of the solid.
right hexagonal prism
14. How many lateral faces does the solid have? 6
15. What kind of figure is each lateral face? rectangle
AVERAGE
q
STUDYING PRISMS Use the diagram at the right.
P
R
V
S
T
B
C
A
D
16. Name four lateral edges.
F
E
Æ Æ Æ Æ Æ
Æ
any 4 of AP , BQ , CR , DS , ET , or FV
ANALYZING NETS Name the solid that can be folded from the net.
Day 1: pp. 732–734 Exs. 18–42
even, 44–47, 50–60
ADVANCED
Day 1: pp. 732–734 Exs. 18–42
even, 44–60
17.
18.
19.
BLOCK SCHEDULE WITH 12.3
pp. 732–734 Exs. 18–42 even,
44–47, 50–60
cylinder
pentagonal prism
triangular prism
SURFACE AREA OF A PRISM Find the surface area of the right prism.
Round your result to two decimal places.
EXERCISE LEVELS
Level A: Easier
13–19
Level B: More Difficult
20–47, 50–60
Level C: Most Difficult
48, 49
20.
ENGLISH LEARNERS
EXERCISES 6–10 If students
have not yet absorbed the terminology for elements of three-dimensional solids, point out on the figure
each element named in Exercises
6–10 before asking students to find
the measurements.
732
22.
10 in.
7m
11 in.
9m
598 in.2
9 in.
HOMEWORK CHECK
To quickly check student understanding of key concepts, go
over the following exercises:
Exs. 14, 18, 22, 28, 32, 36, 38. See
also the Daily Homework Quiz:
• Blackline Master (Chapter 12
Resource Book, p. 36)
•
Transparency (p. 88)
TEACHING TIPS
EXERCISES 17–25 As students
work with nets, encourage them to
use or make a physical model if they
are having trouble seeing how a net
will fold. Also, if students are having
trouble keeping track of all of the
faces of a solid when finding surface
area, encourage them to draw a net
of the solid and find the total area of
all the bases and faces.
21.
23.
2m
6 ft
14 ft
190 m2
98兹3苶 + 252 ≈ 421.74 ft 2
25.
24.
2.9 cm
6m
6.4 cm
7.2 m
6.1 in.
2 cm
4m
2 in.
56.61 cm2
16兹2苶 + 115.2 ≈ 137.83 m2
12兹3苶 + 73.2 ≈ 93.98 in.2
SURFACE AREA OF A CYLINDER Find the surface area of the right cylinder.
Round the result to two decimal places.
26.
27.
28.
6.2 in.
8 cm
10 in.
8 cm
6 ft
STUDENT HELP
HOMEWORK HELP
Example 1: Exs. 13–16,
20–25
Example 2: Exs. 20–25,
29–31, 35–37
Example 3: Exs. 26–28
Example 4: Exs. 32–34
256π ≈ 804.25 cm2
204π ≈ 640.88 ft 2
81.22π ≈ 255.16 in.2
VISUAL THINKING Sketch the described solid and find its surface area.
29–31. See margin.
29. Right rectangular prism with a height of 10 feet, length of 3 feet, and
width of 6 feet
30. Right regular hexagonal prism with all edges measuring 12 millimeters
31. Right cylinder with a diameter of 2.4 inches and a height of 6.1 inches
732
Chapter 12 Surface Area and Volume
29–31. See Additional Answers
beginning on page AA1.
xy USING ALGEBRA Solve for the variable given the surface area S of the
right prism or right cylinder. Round the result to two decimal places.
32. S = 298 ft2 11 ft
33. S = 870 m2 27 m
12 m
34. S = 1202 in.2
7.5 in.
5m
x
z
y
7 ft
18.01 in.
4 ft
LOGICAL REASONING Find the surface area of the right prism when the
height is 1 inch, and then when the height is 2 inches. When the height
doubles, does the surface area double? 35–37. See margin.
35.
36.
2 in.
37.
CAREER NOTE
EXERCISES 38–40
Additional information about
architects is available at
www.mcdougallittell.com.
2 in.
3 in.
1 in.
COMMON ERROR
EXERCISES 26–28 As students
find the surface area of a cylinder,
alert them to avoid several common
errors: forgetting to include the
areas of both bases, using a
diameter instead of a radius, using
the square of the radius value in
both expressions, or multiplying the
height by the area of a base instead
of by its circumference.
1 in.
1 in.
35. 16 in.2; 24 in.2; no
FOCUS ON
CAREERS
PACKAGING In Exercises 38–40, sketch the box that results after the
net has been folded. Use the shaded face as a base. 38–40. See margin.
38.
39.
9兹3苶
36. }
+ 9 ≈ 12.9 in.2;
4
9兹3苶
} + 18 ≈ 21.9 in.2; no
4
40.
37. 12兹3苶 + 12 ≈ 32.8 in.2;
12兹3苶 + 24 ≈ 44.8 in.2; no
38.
41. CRITICAL THINKING If you were to unfold a cardboard box, the cardboard
would not match the net of the original solid. What sort of differences would
there be? Why do these differences exist?
RE
FE
L
AL I
42.
ARCHITECTURE A skyscraper is a rectangular prism with a height
of 414 meters. The bases are squares with sides that are 64 meters. What is
the surface area of the skyscraper (including both bases)? 114,176 m2
43.
WAX CYLINDER RECORDS The first versions of
phonograph records were hollow wax cylinders. Grooves
were cut into the lateral surface of the cylinder, and the
cylinder was rotated on a phonograph to reproduce the
sound. In the late 1800’s, a standard sized cylinder was
about 2 inches in diameter and 4 inches long. Find the
exterior lateral area of the cylinder described. 8π ≈ 25 in.2
ARCHITECTS
use the surface
area of a building to help
them calculate the amount
of building materials needed
to cover the outside of a
building.
41. At least two sides
would be longer or
wider than the
corresponding sides of
the folded box.
Several sides have to
fold over to enclose
the box and make its
structure more rigid.
44.
CAKE DESIGN Two layers of a cake are right
regular hexagonal prisms as shown in the diagram.
Each layer is 3 inches high. Calculate the area of
the cake that will be frosted. If one can of frosting
will cover 130 square inches of cake, how many
cans do you need? (Hint: The bottom of each layer
will not be frosted and the entire top of the bottom
layer will be frosted.) 219兹3苶 + 288 ≈ 667 in.2; 6 cans
39, 40. See Additional Answers
beginning on page AA1.
ADDITIONAL PRACTICE
AND RETEACHING
For Lesson 12.2:
5 in.
11 in.
12.2 Surface Area of Prisms and Cylinders
733
• Practice Levels A, B, and C
(Chapter 12 Resource Book,
p. 13)
• Reteaching with Practice
(Chapter 12 Resource Book,
p. 29)
•
See Lesson 12.2 of the
Personal Student Tutor
For more Mixed Review:
•
Search the Test and Practice
Generator for key words or
specific lessons.
733
Test
Preparation
4 ASSESS
DAILY HOMEWORK QUIZ
Transparency Available
1. How many lateral faces and
how many lateral edges does
an oblique octagonal prism
have? 8, 8
2. Find the surface area of the
right prism. Round your result
to two decimal places.
MULTI-STEP PROBLEM Use the following information.
1.5 in.
A canned goods company manufactures cylindrical
cans resembling the one at the right.
47. Let r, h, and S be the
33π
4 in.
radius, height, and surface 45. Find the surface area of the can. }
} ≈ 52 in.2
2
area of the original
cylinder. Then the surface 46. Find the surface area of a can whose radius and
height are twice that of the can shown. 66π ≈ 207 in.2
area of the larger cylinder
is 2π(2r) 2 + 2π(2r)(2h) =
47. Writing Use the formula for the surface area of a right cylinder to explain
8πr 2 + 8πrh =
why the answer in Exercise 46 is not twice the answer in Exercise 45.
4(2πr 2 + 2πrh) = 4S.
★ Challenge
FINDING SURFACE AREA Find the surface area of the solid. Remember to
include both lateral areas. Round the result to two decimal places.
48. 196 cm2
49.
2 cm
1 in.
28π ≈ 87.96 in.2
3 cm
10 cm
6 cm
3 cm
6 in.
8 cm
213.57 cm 2
EXTRA CHALLENGE
3. Find the surface area of a
right cylinder that has a base
diameter of 8 inches and a
height of 15 inches. Round
your result to two decimal
places. 477.52 in.2
4. Solve for the variable given
that the surface area of the
right prism is 208 m 2.
6m
xm
4 cm
MIXED REVIEW
EVALUATING TRIANGLES Solve the right triangle. Round your answers to
two decimal places. (Review 9.6)
50. m™A = 61°, BC ≈
9.02, AB ≈ 10.31
50. A
51. m™A = 58°, BC ≈
16.80, AB ≈ 19.81
5
52. m™B = 44°, BC ≈
12.43, AB ≈ 17.27
8m
4
5 cm
www.mcdougallittell.com
53. 1805 cos 36° sin 36° ≈
858.33 m 2
51.
52.
A
C
12
10.5
29ⴗ
C
B
B
32ⴗ
C
A
46ⴗ
B
FINDING AREA Find the area of the regular polygon or circle. Round the
result to two decimal places. (Review 11.2, 11.5 for 12.3)
53.
54.
55.
28 ft
54. 196π ≈ 615.75 ft2
55. 96兹3苶 ≈ 166.28 in.2
8 in.
19 m
EXTRA CHALLENGE NOTE
Challenge problems for
Lesson 12.2 are available in
blackline format in the Chapter 12
Resource Book, p. 33 and at
www.mcdougallittell.com.
ADDITIONAL TEST
PREPARATION
1. WRITING Explain how the
formula S = 2B + Ph applies to
finding the surface areas both
of right prisms and of right
cylinders.
See sample answer at right.
734
FINDING PROBABILITY Find the probability that a point chosen at random
Æ
on PW is on the given segment. (Review 11.6)
P
q
0
5
Æ
Æ
56. QS
9
}} ≈ 41%
22
734
R
57. PU
S
U
V
10
15
20
Æ
Æ
Æ
58. QU
8
}} ≈ 73%
11
T
7
}} ≈ 64%
11
59. TW
4
}} ≈ 36%
11
W
60. PV
10
}} ≈ 91%
11
Chapter 12 Surface Area and Volume
Additional Test Preparation Sample answer:
1. Since B represents the area of a base, 2B gives the
total area of both bases either of a prism or a cylinder.
To find B, use the area formula appropriate to a base
with a given shape. Then Ph, the perimeter times the
height, represents the lateral area of either a prism
or cylinder. In the case of a cylinder, the perimeter is
actually the circumference C.