Skills Check

Skills Check

Question 18.1

1. A quarter and a nickel are

  1. geometrically similar because they both have the same shape (a squashed cylinder).
  2. not geometrically similar because they have different denominations.
  3. not geometrically similar because the quarter has a greater diameter while the nickel is thicker.

1.

c

Question 18.2

2. A scale model of a carillon stands 10 in. tall, and the actual carillon stands 100 ft tall. The linear scaling factor of the carillon compared with its model is _____________.

766

2.

120

Question 18.3

3. A popular scale for diecast toy model cars is 1 to 18. If the actual car has a length of 15 ft, what should be the length of the model?

  1. 10 in.
  2. 15 in.
  3. 18 in.

3.

a

Question 18.4

4. You want to enlarge a 2-in. by 3-in. photograph to a 5-in. by 7-in. copy. Assuming that the cost of photographic paper is proportional to its area and that 2-in. by 3-in. reprints cost 40 cents each, you would expect to pay ________________ for the large copy.

4.

$2.33

Question 18.5

5. If a medium 10-in. pizza costs $10 and a similar 12-in. pizza costs $14, which costs less per square inch?

  1. The 10-in. pizza
  2. They are about the same price per square inch.
  3. The 12-in. pizza

5.

b

Question 18.6

6. An artist plans to melt 1000 pennies and re-form a larger penny proportional in all dimensions to an ordinary penny. The linear scaling factor of the large penny compared with the ordinary penny is __________.

6.

10

Question 18.7

7. The actor Elijah Wood, who plays Frodo Baggins in the movie version of J. R. R. Tolkien’s The Hobbit, is 5 ft 6 in. tall, but his character is barely 4 ft tall. Put correctly, how much shorter is Frodo than Wood?

  1. 138% shorter
  2. 73% shorter
  3. 27% shorter

7.

c

Question 18.8

8. In December 2014, the telescope on NASA’s Kepler spacecraft discovered a planet 180 light years away that has a diameter 2.5 times that of Earth. Assuming the same density as Earth, the newly discovered planet would have a mass about _________ times that of Earth.

  1. 2.5
  2. 6
  3. 15

8.

c

Question 18.9

9. Which of the following is precise language to express the comparison that Ahmed has $100 and Burke has $50?

  1. Ahmed has 100% more than Burke.
  2. Burke has 200% less than Ahmed.
  3. Burke has twice as less as Ahmed.

9.

a

Question 18.10

10. The Apple iPhone 6 Plus features a screen with 1920 physical pixels vertically and 1080 pixels horizontally, the same as “Full HDTV” high-definition video. For the iPhone screen to be geometrically similar to a 720p high-definition (just “HD”) screen, which has 720 pixels horizontally, the high-definition screen would have to have _____________ pixels vertically (which it does).

10.

1280

Question 18.11

11. A kilometer is approximately equal in length to

  1. 5 mi.
  2. 3 mi.
  3. 3/5 mi.

11.

c

Question 18.12

12. The distance for the marathon race was established in 1921 as 42.195 km. Converted to the U.S. customary system, the distance is ___________________.

12.

26.2187575 mi (officially, 26 mi and 385 yd)

Question 18.13

13. A 2-liter bottle contains approximately

  1. 2 quarts.
  2. 1 gallon.
  3. 10 pints.

13.

a

Question 18.14

14. A weight of 130 lb is approximately the same as ____________ kg.

14.

60

Question 18.15

15. Coffee costs about $10 per pound in the United States. If a Canadian dollar (CAD$) exchanges for U.S. $0.86, what is the approximate equivalent cost in Canadian dollars of 500 g of coffee?

  1. CAD $9
  2. CAD $10
  3. CAD $13

15.

c

Question 18.16

16. A common speed limit in European neighborhoods is 30 km/h, which is about ____________ mph.

16.

19

Question 18.17

17. Which of the following is a unit in the metric system?

  1. minimeter
  2. miniliter
  3. millimeter

17.

c

Question 18.18

18. A mile is approximately __________ km.

18.

1.6

Question 18.19

19. A speed of 60 mph is approximately

  1. mm/min.
  2. 90 ft/s.
  3. 50 m/s.

19.

b

Question 18.20

20. A sculpture weighs 140 lb and is supported by three legs, each of which is 0.5 in. by 0.5 in. by 2 in. high. The legs exert a pressure of approximately ____________ on the floor.

20.

200

Question 18.21

21. The mass of a scaled-up object goes up with the

  1. square root of the volume.
  2. square of the linear scaling factor.
  3. density.

21.

c

Question 18.22

22. In comparing flight speeds of birds, an analysis of wing loading leads to the conclusion that ___________ birds need to fly faster than ___________ birds.

22.

heavy (or big); light (or small)

Question 18.23

23. Scaling analysis leads to the general conclusion that

  1. smaller animals can jump much higher than larger animals.
  2. larger animals can jump much higher than smaller animals.
  3. all animals can jump to about the same height.

767

23.

c

Question 18.24

24. If an object is scaled linearly so that its volume grows to 8 times its original volume, its surface area is scaled to ________ times its original surface area.

24.

4

Question 18.25

25. A large change in scale forces a change in

  1. form.
  2. form and materials.
  3. form or materials.

25.

c

Question 18.26

26. Assuming that a catfish maintains the same shape and proportions as its grows, and that a catfish 8 in. long weighs about 1 lb, a 2-lb catfish would be about ________ in. long.

26.

10

Question 18.27

27. Metabolic rate scales as the _________ power of mass.

  1. one-third
  2. two-thirds
  3. three-quarters

27.

c

Question 18.28

28. The base-10 logarithm of 1000 is ______.

28.

3

Question 18.29

29. The population of Mexico is expected to grow 1.2% per year from 2015 through 2018. The population will be growing

  1. proportionally.
  2. allometrically.
  3. by a constant amount each year.

29.

a (or b)

Question 18.30

30. Allometric growth is growth of the length of one feature at a rate _________ the length of another.

30.

proportional to a power of