Name ———————————————————————
LESSON
12.3
Date ————————————
Challenge Practice
For use with pages 842–849
1. The slant height of a right cone is twice the radius of the cone. The surface area
of the cone is 75π square inches. Find the slant height and radius of the cone.
2. The slant height of a square pyramid is 6 more than the length of a side of the base.
The surface area of the pyramid is 231 square centimeters. Find the slant height and
the length of a side of the base of the pyramid.
In Exercises 3–7, use the following information.
The frustum of a cone is formed by cutting the top off of a cone,
with a cut parallel to the base. In the figure at the right, r is the
radius of the top of the frustum, R is the radius of the bottom,
h is the height, and l is the slant height.
r
h
3. Derive a formula for the surface area S of a frustum of a
cone in terms of r, R, and l.
R
4. Rewrite the formula from Exercise 3 in terms of r, R,
and h.
5. Find the surface area of the frustum of a cone with r 5 6 feet, R 5 8 feet, and
l 5 13 feet.
6. Find the surface area of the frustum of a cone with r 5 2.1 meters, R 5 7.9 meters,
and h 5 12.2 meters.
7. The surface area of the frustum of a cone is 98π square yards, r 5 3 yards, and
l 5 8 yards. Find R.
The frustum of a pyramid is formed by cutting the top off of a
pyramid, with a cut parallel to the base. In the figure at the right,
h is the height and l is the slant height.
8. Derive a formula for the surface area S of the frustum of
h
a pyramid.
9. Find the surface area of a frustum of a pyramid that has
a square base with side length of 12 meters, a square top
with side length of 5 meters, and a slant height of 14 meters.
10. Find the surface area of a frustum of a pyramid that has a regular hexagonal base
with side length of 6 feet, a regular hexagonal top with side length of 1 foot, and a
slant height of 7 feet.
11. The surface area of a frustum of a pyramid with a square base and a square top is
4156 square millimeters. The slant height of the frustum is 30 millimeters and the
side length of the top of the frustum is 10 millimeters. Find the side length of the
base of the frustum.
Geometry
Chapter 12 Resource Book
LESSON 12.3
Copyright © Holt McDougal. All rights reserved.
In Exercises 8–11, use the following information.
417
Lesson 12.3, continued
24. 72 m2
25. 819.96 ft2
18. 14,003.96 in.2 19. 711.37 m2
20. 458.4 m2
20 ft
10 m
20.34 yd
4m
9 ft
26. 3817.04 cm2 27. 12,315.04 in.2 28. 6 ft
Practice Level B
Review for Mastery
4. Check sketches; 189 m2; 140 m2.
1. 37.5 m2 2. 337.5 m2; 187.5 m2
5. Check sketches; 588.44 ft2; 378.00 ft2.
3. Lateral area 5 260π < 816.8 yd2
6. Check sketches; 287.68 cm2; 214.5 cm2.
4. S 5 360π < 1131.0 yd2
7. 157.08 m2
8. 188.5 ft2 9. 304.52 cm2 10. 578.05 m2
11. 440.67 ft
2
12. 1160.06 cm
2
Problem Solving Workshop:
Mixed Problem Solving
13. C
1. a. rectangle b. 24 in., 32 in.2
c. right triangles d. 16 in.2 2. The candle shaped
15. 252.85 in.2
14. 756 in.
12 in.
10 in.
12 in.
18 in.
12 in.
16. 117.69 ft2
22. 178.67 cm2 23. 23,071.86 in.2
24. 1181.36 ft2
1. 12 m2 2. 48 ft2 3. 232.05 cm2
2
16.90 yd
8m
12 in.
17. 282.74 m2
3 ft
12 m
9 ft
like a cone needs to have more plastic wrapped
around it because it has a larger surface area than
the candle shaped like a regular square pyramid.
3. a. 600 m2 b. Double each side of the base.
c. Double each side of the base: 1440 m2, double
the height: 1080 m2; Doubling each side of the
base creates a greater surface area than doubling
the height. 4. a. 360 ft2 b. 2 c. about 128.1 ft2
d. 2 5. Answers will vary. 6. 16.3 ft2
Challenge Practice
9m
1. Slant height: 10 in.; radius: 5 in.
2. Slant height: 13 cm; side length of base: 7 cm
18. 480 m2 19. 119.38 in.2 20. 124.71 cm2
21. 611.76 ft 22. 231,243.64 ft2
1
7. R 5 5 yd 8. S 5 B1 1 B2 1 } (P1 1 P2)l,
2
Practice Level C
1. 25.46 cm2 2. 251.56 ft2 3. 134.23 m2
2
2
4. Check sketches; 124.99 m ; 88.99 m .
5. Check sketches; 171.83 cm2; 126 cm2.
6. Check sketches; 134.61 ft2; 110.25 ft2.
7. Check sketches; 671.06 yd2; 362.04 yd2.
8. Check sketches; 508.71 m2; 358.11 m2.
9. Check sketches; 125.12 in.2; 93.83 in.2.
10. 353.69 m2 11. 157.63 yd2 12. 332.35 mm2
13. 298.45 cm2 14. 170.99 m2 15. 352.58 cm2
16. 1487.93 ft2 17. 126.67 yd2
Geometry
Chapter 12 Resource Book
}}
4. S 5 π(r 1 R)Ï (R 2 r)2 1 h2 1 πr2 1 πR2
5. 282π < 885.9 ft2 6. about 634.3 m2
23. 924,974.57 ft2
A60
3. S 5 π(r 1 R)l 1 πr 2 1 πR2
where B1 is the area of the base, B2 is the area of
the top, P1 is the perimeter of the base, P2 is the
perimeter of the top, and l is the slant height.
111 }
9. 645 m2 10. 147 1 }Ï 3 < 243.1 ft2
2
11. 36 mm
Lesson 12.4
Practice Level A
1. 40 cubic units 2. 240 cubic units
3. 84 cubic units 4. 8 ft3 5. 105 m3 6. 40 cm3
Copyright © Holt McDougal. All rights reserved.
ANSWERS
7m
21. 809.01 yd2