Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find the length of an arc
intercepted by a central angle è in a circle of radius r.
Round your answer to 1 decimal place.
r = 16.12 ft; è =
 radians
a. | 2.3 ft | c. | 9.2 ft | b. | 13.8 ft | d. | 4.6 ft |
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2.
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Find the length of an arc
intercepted by a central angle è in a circle of radius r.
Round your answer to 1 decimal place.
r = 16.05 cm.; è
=  ð
radians
a. | 21.4 cm | c. | 134.5 cm | b. | 67.2 cm | d. | 33.6 cm |
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3.
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Find the length of an arc
intercepted by a central angle è in a circle of radius r.
Round your answer to 1 decimal place.
r = 115.19 in.; è
= 195°
a. | 196.0
in. | c. | 784.1
in. | b. | 124.8 in. | d. | 392.0 in. |
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4.
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Assume that the cities lie
on the same north-south line and that the radius of the earth is 6400 km.
Find the distance between City A, 34° N and City B, 37° N. (Round
to the nearest kilometer.)
a. | 406 km | c. | 372 km | b. | 301 km | d. | 335 km |
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5.
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Assume that the cities lie
on the same north-south line and that the radius of the earth is 6400 km.
Find the distance between City E, 35° N and City F, 44° S. (Round to
the nearest kilometer.)
a. | 997 km | c. | 8832 km | b. | 1005 km | d. | 8824 km |
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6.
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Assume that the cities lie
on the same north-south line and that the radius of the earth is 6400 km.
Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, 
are  apart.
a. | 52.46
°N | c. | 47.5
°N | b. | 39.5 °N | d. | 38.8 °N |
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7.
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Assume that the cities lie
on the same north-south line and that the radius of the earth is 6400 km.
Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX,  ,
are  apart.
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8.
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A pendulum of length 12.1
inches swings 5° to each side of its vertical position. What
is the length (to the nearest hundredth of an inch) of the arc through which the end of the pendulum
swings?
a. | 2.07
in. | c. | 2.27
in. | b. | 2.17 in. | d. | 2.37 in. |
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9.
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A pendulum swinging through a
central angle of 67° completes an arc of length 7.2 cm. What is the length of the
pendulum? Round to the nearest hundredth.
a. | 6.06 cm | c. | 6.16 cm | b. | 5.96 cm | d. | 6.26 cm |
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10.
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A bicycle with a 26-inch
wheel (diameter) travels a distance of 200 feet. How many revolutions does the wheel make (to
the nearest revolution)?
a. | 52
revolutions | c. | 23
revolutions | b. | 58 revolutions | d. | 29 revolutions |
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11.
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A car wheel has a 14-inch
radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls
forward 3 ft?
a. | 152.3° | c. | 162.3° | b. | 157.3° | d. | 147.3° |
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12.
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A wheel with a 36-inch
radius is marked at two points on the rim. The distance between the marks along the wheel is found to
be 12 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two
marks?
a. | 15.1° | c. | 19.1° | b. | 21.1° | d. | 17.1° |
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13.
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Electrical wire is being wound
around a drum with radius of 1.49 meters. How much line (to the nearest hundredth of a meter)
would be wound around the drum if it is rotated through an angle of 
a. | 7.16 m | c. | 7.06 m | b. | 7.26 m | d. | 6.96 m |
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14.
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Two wheels are rotating in such
a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the
smaller wheel is  and the radius of the larger wheel is  Through how many degrees (to the nearest hundredth of a degree) will the larger wheel
rotate if the smaller one rotates 
a. | 93.73° | c. | 94.73° | b. | 93.63° | d. | 95.73° |
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15.
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Find the radius (to the nearest
hundredth of a millimeter) of a pulley if rotating the pulley 109.38° raises the
pulley 42.2 mm.
a. | 22.01
mm | c. | 21.91
mm | b. | 22.11
mm | d. | 22.21 mm |
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16.
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A pulley with a diameter
of 26 inches is driven by a belt which is moving 859 ft/min. To the nearest unit, how
many revolutions per minute are made by the pulley?
a. | 224 rpm | c. | 138 rpm | b. | 231 rpm | d. | 126 rpm |
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17.
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A pulley rotates through
57° in one minute. How many rotations (to the nearest tenth of a rotation) does the pulley make
in an hour?
a. | 342.0
rotations | c. | 19.0
rotations | b. | 9.5 rotations | d. | 171.0 rotations |
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18.
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Suppose the tip of the minute
hand of a clock is 6 inches from the center of the clock. Determine the distance traveled by
the tip of the minute hand in 30 minutes. Give an exact answer.
a. | 3ð
in. | c. | 36ð
in. | b. | 6ð in. | d. | 12ð in. |
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19.
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Suppose the tip of the minute
hand of a clock is 15 inches from the center of the clock. Determine the distance traveled by
the tip of the minute hand in 10 minutes. Give an exact answer.
a. | 25ð
in. | c. | 10ð
in. | b. | 5ð in. | d. | 2.5ð in. |
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20.
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Suppose the tip of the minute
hand of a clock is 5 inches from the center of the clock. Determine the distance traveled by
the tip of the minute hand in 5.5 hours. Give an exact answer.
a. | 25ð
in. | c. | 55ð
in. | b. | 50ð in. | d. | 30ð in. |
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21.
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Suppose the tip of the minute
hand of a clock is 5 in. from the center of the clock. Determine the distance traveled by the
tip of the minute hand in  hours. Give an exact
answer.
a. | 15ð
in. | c. | 20ð
in. | b. | 35ð in. | d. | 30ð in. |
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22.
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The minute hand of a clock
is 13 inches long. What distance does its tip move in 16 minutes? Give an exact
answer.
a. |  ð in. | c. |  ð
in. | b. |  ð
in. | d. |  ð in. |
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23.
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Approximate the length using
the formula for arc length. Round to the nearest meter.
A tree 460 m away subtends an angle of
2°. Find the height of the tree.
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24.
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Approximate the length using
the formula for arc length. Round to the nearest meter.
A television tower 540 m high subtends an angle
of 3° . How far away is the
tower?
a. | 4900 m | c. | 8111 m | b. | 8071 m | d. | 4860 m |
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25.
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Find the area of a sector of
a circle having radius r and central angle è. If necessary,
express the answer to the nearest tenth.
r = 44.6 cm, è
=  radians
a. | 76.5
cm2 | c. | 480.8
cm2 | b. | 240.4 cm2 | d. | 5.4 cm2 |
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26.
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Find the area of a sector of
a circle having radius r and central angle è. If necessary,
express the answer to the nearest tenth.
r = 7.0 ft, è
=  radians
a. | 15.4
ft2 | c. | 7.3
ft2 | b. | 51.3 ft2 | d. | 102.6 ft2 |
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27.
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Find the area of a sector of
a circle having radius r and central angle è. If necessary,
express the answer to the nearest tenth.
r = 19.0 m, è
= 20°
a. | 0.6 m2 | c. | 126.0 m2 | b. | 3.3 m2 | d. | 63.0 m2 |
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28.
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Find the area of a sector of
a circle having radius r and central angle è. If necessary,
express the answer to the nearest tenth.
r = 7.4 mi, è
= 314°
a. | 55.6
mi2 | c. | 150.1
mi2 | b. | 300.1 mi2 | d. | 20.3 mi2 |
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29.
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Find the radius of a circle in
which a central angle of  radian determines a sector of area  meters. Round to the nearest hundredth.
a. | 9.42 m | c. | 13.33 m | b. | 18.85 m | d. | 177.62 m |
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30.
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Find the measure (in radians)
of a central angle of a sector of area 55 square inches in a circle of radius 8 inches.
Round to the nearest hundredth.
a. | 3.44
radians | c. | 0.86
radians | b. | 2.58 radians | d. | 1.72 radians |
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31.
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A pendulum swings through an
angle of 18° each second. If the pendulum is 20 cm in length and the complete swing
from right to left lasts 2 seconds, what area is covered by each complete swing? Round to the
nearest hundredth.
a. | 6.28  | c. | 62.83  | b. | 125.66  | d. | 251.33  |
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32.
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What is the difference in area
covered by a single 12-inch windshield wiper operating with a central angle of 
compared to a pair of 2-inch wipers operating together each having a central angle of  Round to the nearest hundredth.
a. | 150.80  | c. | 165.88  | b. | 155.80  | d. | 154.57  |
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33.
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A sensor light installed on the
edge of a home can detect motion for a distance of  in front and with a range
of motion of  Over what area will the sensor detect
motion and become illuminated? Round to the nearest hundredth.
a. | 21,770.92  | c. | 10,885.46  | b. | 21,771.02  | d. | 10,885.36  |
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34.
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A center-pivot irrigation
system waters a sector-shaped field. Find the area of the field if the central angle,
è = 44° and the radius,  Round to the
nearest whole number.
a. | 114  | c. | 57  | b. | 16,821  | d. | 8411  |
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35.
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A circular sector has an area
of 486  . The radius of the circle is 9 feet.
What is the arc length of the sector?
a. | 110 ft | c. | 108 ft | b. | 12 ft | d. | 54 ft |
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36.
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A circular sector has an area
of 18  and an arc length of 3 inches. What is
the measure of the central angle in degrees? Round to the nearest degree.
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