Name ———————————————————————
LESSON
12.2
Date ————————————
Challenge Practice
For use with pages 834–841
1.
2.
3.
8 cm
45 ft
25 in.
13 cm
24 ft
5 cm
7 in.
12 in.
LESSON 12.2
In Exercises 1–3, find the surface area of the oblique prism or cylinder.
27 ft
6 in.
32 ft
4. The figure at the right shows the diagonal of a right
rectangular prism. Derive a formula for finding the
length of the diagonal d.
5. Use your formula from Exercise 4 to find the length
of the diagonal of a right rectangular prism with
length 6 inches, width 3 inches, and height 5 inches.
h
d
w
l
6. Use your formula from Exercise 4 to find the height of a right rectangular
prism with diagonal length 35 centimeters, length 16 centimeters, and width
12 centimeters.
7. What happens to the length of the diagonal if you double the length, width,
and height of a right rectangular prism?
8. The height of a right rectangular prism is twice the width and the length is
Copyright © Holt McDougal. All rights reserved.
three times the width. The surface area is 88 square yards. Find the length,
width, and height of the prism.
In Exercises 9 and 10, find the height and radius of the right
circular cylinder.
9. S 5 44π ft2
10. S 5 884π cm2
4x 2 3
x15
2x 1 1
x22
Geometry
Chapter 12 Resource Book
407
Lesson 12.2, continued
15. Check sketches; 154 yd2; 56 yd2.
12. 6940.8 cm2; 5177.97 cm2 13. 3583.49 in.2
16. Check sketches; 3600 in.2; 2800 in.2.
14. 3160.46 mm2 or 31.6 cm2 15. 402.42 m2
17. Check sketches; 167.66 m2; 138 m2.
16. 4.42 ft 17. 13.8 m 18. 5.75 yd
2
18. Check sketches; 275.14 ft ; 192 ft .
19. 1130.04 ft2 20. 5288.16 m2 21. 5 cm
19. 100.53 cm2; 75.40 cm2
22. 3 yd 23. 96 ft2
20. 904.78 ft2; 395.84 ft2
24. 301.59 m2 25. 82 cm2
21. 6880.09 m2; 5466.37 m2
26. 1163.96 yd2
22. 835.66 yd2; 527.79 yd2
Review for Mastery
23. 30,259.82 in.2; 25,333.80 in.2
2
24. 7.85 mm ; 6.28 mm
ANSWERS
2
1. 184 in.2; 144 in.2
2
2. 768π < 2412.74 cm2; 1507.96 cm2 3. 21 ft
2
25. 3 ft 26. 9 cm 27. 14 cm 28. 276 m
Problem Solving Workshop:
Using Alternative Methods
29. 33.8 cm2 30. 5 ft 31. 6 mm
1. 972 in.2 2. 860.55 m2
Practice Level B
1. Check sketches; 162 cm2
Challenge Practice
2. Check sketches; 4656 in.2
3. Check sketches; 345.58 ft
1. 1020 in.2 2. 320π < 1005 cm2 3. 6000 ft2
}}
2
}
4. d 5 Ï l2 1 w 2 1 h2 5. Ï 70 < 8.4 in.
}
4. Check sketches; 248 m2; 168 m2.
6. Check sketches; 228.06 cm2; 150 cm2.
6. 5Ï 3 < 28.7 cm 7. The diagonal length
doubles. 8. Length: 6 yd; width: 2 yd;
height: 4 yd 9. Height: 9 ft; radius: 2 ft
7. 628.32 cm2; 471.24 cm2
10. Height: 21 cm; radius: 13 cm
5. Check sketches; 309.21 ft2; 269.21 ft2.
8. 29.72 ft2; 22.12 ft2
Lesson 12.3
9. 2261.95 in.2; 1357.17 in.2
Practice Level A
10. 8 m 11. 10.23 ft 12. 11.89 cm
1.
13. S 5 2xy 1 2xz 1 2yz 14. 216 in.2
slant
height
height
Copyright © Holt McDougal. All rights reserved.
15. 184 in.2 16. B
1
17. The new surface area is } of the original
4
base
surface area.
18. 3 ft 19. 207.35 in.2 20. 2.5 ft
21. 70.69 ft2 22. 117.81 ft2
2. regular pentagon 3. triangle 4. 5
} } }
5. Sample answer: AC, AB, AE 6. 45 m2
7. 84 ft2 8. 260 cm2
Practice Level C
9. Check sketches; 64 yd2; 48 yd2.
1. Check sketches; 570.89 ft
2
2. Check sketches; 102.22 m
10. Check sketches; 52.2 m2; 42 m2.
2
3. Check sketches; 671.17 cm
11. Check sketches; 135.7 ft2; 108 ft2.
2
12. Check sketches; 547.5 cm2; 375 cm2.
2
2
4. Check sketches; 150.01 cm ; 89.87 cm .
2
13. Check sketches; 1536 yd2; 960 yd2.
2
5. Check sketches; 140.12 m ; 113.66 m .
2
14. Check sketches; 296.4 in.2; 234 in.2.
2
6. Check sketches; 29.76 mi ; 10.54 mi .
2
15. 329.87 in.2 16. 188.5 m2
2
7. Check sketches; 1984.5 in. ; 1488.38 in. .
2
2
17. 508.94 cm2 18. 251.33 yd2
2
8. Check sketches; 53.83 ft or 5.98 yd ; 42 ft
or 4.67 yd2.
9. Check sketches; 508.88 ft2; 334.08 ft2.
10. 1.52 m2; 1.13 m2 11. 1198.69 ft2; 391.65 ft2
19. 1046.15 m2 20. 2060.88 mm2
21. 761.05 in.2 22. 703.72 m2
23. 221.19 cm2
Geometry
Chapter 12 Resource Book
A59