1. Surface Areas of Pyramids and Cones
GEOMETRY LESSON 10-4 m2
,308 ft2
ft2
cm2
ft2
cm2 m m yd
Pages Exercises
in.2 m2
cm2
21. Answers may vary. Sample: PT < PR, since PR is a hyp. in
PTR. m PCR = m PBR (since
PCB is isosc.) and m PBR <
m PRC, so
m PCR < m PRC. Therefore, PR < PC.
in.2 m2
in.2
4. 50 m
5. 12 in.
6. 4 m m2
cm2
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2. Surface Areas of Pyramids and Cones
GEOMETRY LESSON 10-4
22. Altitude; altitude; the altitude is shorter because it is one
leg of a right with the lateral edge as the hyp., and is steeper because it rises the same vert. distance over less horiz. distance.
in.2
24. 8 ft
cm2
cm2
in.2
28. 4 in.
29. Answers may vary. Sample:
29. (continued)
64 cm2
ft2 m2
ft2 m2
34. Cylinder: the lateral area of the 2 cones is in.2 and the lateral area of the cylinder is in.2.
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3. Surface Areas of Pyramids and Cones
GEOMETRY LESSON 10-4
38. s = 2 ft,
h = 4.9 ft,
S.A. = 24 ft2
39. s = 8 cm,
= 7.4 cm,
h = 6.2 cm
= 2.3 ft,
C = 18.8 ft,
L.A. = 21.7 ft
= 6.5 m,
C = 25.1 m,
S.A. =132.0 m2
42. r = 7.0 in.,
42. (continued)
= 8.0 in.,
S.A. = in.2
43. r = 1.0 ft,
S.A. = 36.4 ft2,
C = 6.3 ft cm
45. about cm2
46. cone with r = 4 and h = 3; 36
47. cone with r = 3 and h = 4; 24
35. ( + r)r = r +
r2, which is the lateral area plus the circular base area. This formula may require fewer keystrokes and doesn’t use exponents.
36. L.A. = 30 in.2, h = 4.8 in., = 5 in.
37. s = 12 m,
L.A. = 240 m2,
S.A. = 384 m2
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4. Surface Areas of Pyramids and Cones
GEOMETRY LESSON 10-4
54. 2 : 3
55. A
56. I
57. C
58. F
59. [2] Use the formula for surface area of a pyramid: S.A. = p + B. Subst. the surface area,
59. [2] (continued)
perimeter, and base:
240 =
Solve: = 11.
[1] correct formula with one computational error.
60. [4]
a. L.A. = 2B
r = 2 r2
= 2r
b. L.A. = r
48. cylinder with cone-shaped hole; 60
49. cylinder with cone-shaped hole; 48
cm2;
cm2
cm2;
cm2
53. Check students’ work. 1 2
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5. Surface Areas of Pyramids and Cones
GEOMETRY LESSON 10-4
60. (continued)
[1] correct lateral area without any work shown
ft2
in2
63. about m cm
in.
60. [4] (continued)
b. L.A. = (6)(12)
c. L.A. = cm2
[3] one computational error
[2] correct methods in (a) and (b) but incorrect relationship between and r
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