Name———————————————————————— Date —————————————
Practice B
Lesson
11.9
For use with the lesson “Explore Similar Solids”
Tell whether the pair of right solids is similar. If so, determine the
scale factor.
1.
2.
3 ft
8 cm
2 ft
4 cm
6 cm
Lesson 11.9
3.
7 cm
4 ft
4.
4 mm
4 mm
6 mm
10 mm
6 ft
3 cm
5 mm
4 mm
2m
1.2 m
3m
4.5 m
1.8 m
5. Multiple Choice Which set of dimensions corresponds to a right cylinder that is similar to the cylinder shown?
A. r 5 2, h 5 5
B. r 5 3, h 5 7
C. r 5 10, h 5 19
D. r 5 15, h 5 27
2.7 m
5 in.
9 in.
Solid A (shown) is similar to Solid B (not shown) with the given scale
factor of A to B. Find the surface area and volume of Solid B.
6. Scale factor of 1: 2
7. Scale factor of 1 : 3
8. Scale factor of 2 : 3
S 5 42p ft 2, V 5 36p ft 3 S 5 96p m2, V 5 96 p m3 S 5 75.6 cm2, V 5 36 cm3
A
A
A
9. Finding Surface Area Two spheres have a scale factor of 1 : 3. The smaller sphere
has a surface area of 16π square feet. Find the surface area of the larger sphere.
10. Multiple Choice Two right cylinders are similar. The surface areas are 24π and
96π. What is the ratio of the volumes of the cylinders?
1
1
1
2
​ 8 ​ C. }
​ 2 ​ D. }
​ 3 ​
A. ​ }4 ​ B. }
11-122
Geometry
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
14 cm
Name———————————————————————— Date —————————————
Practice B continued
Lesson
11.9
For use with the lesson “Explore Similar Solids”
Solid A is similar to Solid B. Find the scale factor of Solid A to Solid B.
11.
A
12.
B
S = 208 m2
B
A
S = 52 m2
S = 63p cm2
13.
A
S = 28p cm2
14.
A
V = 27 ft3
B
V = 64 ft3
V = 54 in.3
V = 16 in.3
Solid A is similar to Solid B. Find the surface area and volume of Solid B.
15.
16.
2 3m
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
B
A
4m
Lesson 11.9
B
18 mm
8m
4m
A
12 mm
B
10 mm
4m
17. Finding a Ratio Two cubes have volumes of 64 cubic feet and 216 cubic feet.
What is the ratio of the surface area of the smaller cube to the surface area of
the larger cube?
In Exercises 18–22, use the following information.
Water Tower As part of a class project, you obtain the responsibility of making a scale model of the water tower in your town. The water
tower’s diameter is 12 feet and the height is 16 feet. You decide that
0.5 inch in your model will correspond to 12 inches of the actual
water tower.
12 ft
16 ft
18. What is the scale factor?
19. What is the radius and height of the model?
20. What is the surface area of the model?
21. What is the volume of the actual water tower?
22. Use your result from Exercise 21 to find the volume of the model.
Geometry
Chapter Resource Book
11-123
Lesson 11.9 Explore Similar
Solids, continued
Sample answer:
8. 243 ft2; 182.25 ft3 9. S 5 90 cm2, V 5 50 cm3;
S 5 810 cm2, V 5 1350 cm3 10. S ø 141.4 in.2,
3
4
5
4. Check student’s drawings:
Sample answer:
2
4
Study Guide
Practice Level A
1
1
3
9
1. Not similar; radius }
​ 9 ​5 ​ }3 ​, height }
​ 18  ​ 5 }
​ 2 ​
1. not similar 2. yes; 3 : 2 3. yes; 7 : 4
4. yes; 3 : 2 5. 3 : 1 6. 3 : 1 7. 3 : 1 8. 9 : 1
2
3
9. 27 : 1 10. D 11. S 5 832 m , V 5 1536 m
12. S 5 2464 ft2, V 5 4096 ft3
2
3
13. S 5 202.5π cm , V 5 337.5π cm
14. 1 : 2
2. Similar; The scale factor is 5 : 8. 3. 1 : 2;
}
}
Edge length of C is Ï
​ 6 ​ units; 48​Ï 6 ​ cubic units
Problem Solving Workshop:
Mixed Problem Solving
15. 7 : 2 16. 5 : 6 17. 1 : 4 18. false 19. false
1. a. 10,800 in.3 b. 72 in.3 c. 150
20. false 21. false 22. 4 : 1 23. 3750π yd3
2. a. 576 in.2 b. 2250 in.3 c. 250
24. 13,536 in.2
3. Answers will vary. 4. a. 48.11 in.3 b. yes;
20. 66π in.2 21. 576π ft3 22. 72π in.3
The juice has a volume of about 36.1 in.3, which is
smaller than the volume of the cup.
5. a. The volume doubles. b. The volume
quadruples.
c. You can substitute 2h for h in the formula for
the volume of a right cone and substitute 2r for
r in the same formula and rewrite the formula.
6. 25 in.3 7. a. 25.78 in.2; 12.31 in.3
b. 45.84 in.2; 29.18 in.3 c. 45.84 in.2; 29.18 in.3;
yes
Practice Level C
Challenge Practice
Practice Level B
1. similar; 2 : 1 2. similar; 3 : 2 3. not similar
4. similar; 1 : 0.6 5. D 6. 168π ft2; 288π ft3
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
answers
V ø 109.5 in.3; S ø 2262.4 in.2, V ø 7008 in.3
11. S ø 201.1 ft2, V ø 268.1 ft3; S ø 2463.0 ft2,
V ø 11,494.0 ft3 12. 6: 5 13. 3 : 22 14. 450
15. 686 16. 7 17. 3, 5 18. 728π m2
19. 1920 yd3 20. smaller cylinder: r 5 4 cm,
h 5 8 cm; larger cylinder: r 5 5 cm, h 5 10 cm;
21. 5.8 ft high, 5.5 ft wide, 12.8 ft long
22. 1.56 ft3
7. 864π m2; 2592π m3 8. 170.1 cm2;
121.5 cm3 9. 144π ft2 10. B 11. 2 : 1
12. 2 : 3 13. 3: 4 14. 3 : 2 15. about 385.6 m2;
about 330.98 m3 16. 975π mm2; 4500π mm3
17. 4 : 9 18. 1 : 24 19. r 5 3 in.; h 5 8 in.
1. yes; 1 : 2 2. yes; 1 : 4 3. not similar
4. yes; 5 : 3 5. 256 in.2; 224 in.3
6. 2432π in.2, 15,360π in.3 7. 324 cm3; 1 : 3
7
1. x 5 7 2. x 5 9 3. x 5 4 4. x 5 }
​ 2 ​
11
5. x 5 1 6. x 5 }
​ 2  ​
Geometry
Chapter Resource Book
A67