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WorksheetsAdvMath Unit 21 - Arcs, Sectors, & Velocity
Total questions: 83
Worksheet time: 5hrs 21mins
Name
Class
Date
1.
In circle O, the radius is 4, and the measure of minor arc AB is 120 degrees. Find the length of minor arc AB to the nearest integer.
a)
5
b)
9
c)
8
d)
6
2.
Find the length of the arc.
a)
31.42cm
b)
15.71cm
c)
282.74cm
d)
23.56cm
3.
When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.
a)
40
b)
35
c)
55
d)
69
4.
Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.
a)
9.2 sq. in.
b)
10.5 sq. in.
c)
31.4 sq. in.
d)
38.2 sq. in.
5.
Find the area of the sector with a measure of 60 degrees and radius of 10in.
a)
52.4 in2
b)
18,864 in2
c)
60 in2
d)
10.47 in
6.
Find the area of the sector with a radius of 3m and measure of 150 degrees.
a)
4248 m2
b)
7.9 m2
c)
2827.4 m2
d)
11.8 m2
7.
What is the area of the shaded sector?
a)
339.12 in2
b)
113.04 in2
c)
339.29 in2
d)
None of the above
8.
The diameter of the face-off circle on an ice-hockey rink is 30 feet. Find its area.
a)
675.6 ft2
b)
29.67 ft2
c)
545.8 ft2
d)
706.5 ft2
9.
Alison is jogging on a circular track that has a radius of 140 feet. She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.
a)
47
b)
74
c)
94
d)
123
10.
In circle O, the radius is 4, and the measure of minor arc AB is 120 degrees. Find the length of minor arc AB to the nearest integer.
a)
5
b)
8
c)
9
d)
12
11.
When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.
a)
35
b)
48
c)
65
d)
69
12.
In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree.
a)
60
b)
45
c)
63
d)
81
13.
What is the circumference?
a)
48
b)
96
c)
24
d)
18
14.
What is the radius of this circle?
a)
18
b)
10
c)
9
d)
8
15.
The distance along an arc measured in units is called the ________
a)
area of a sector
b)
arc length
c)
arc of a circle
d)
sector of a circle
16.
Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.
a)
9.2 sq. in.
b)
10.5 sq. in.
c)
31.4 sq. in.
d)
38.2 sq. in.
17.
A cathedral window is built in the shape of a semicircle. If the window is to contain three stained glass sections of equal size, what is the area of each stained glass section? Express answer to the nearest square foot.
a)
1 sq. ft
b)
13 sq. ft
c)
3 sq. ft
d)
26 sq. ft
18.
Find the area of the dark blue sector shown at the left. The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units. Express answer to the nearest tenth of a square unit.
a)
0.3 square units
b)
15.7 square units
c)
19.7 square units
d)
50.3 square units
19.
Find the length of the arc.
a)
31.42cm
b)
15.71cm
c)
282.74cm
d)
23.56cm
20.
Find the length of the arc to 2dp
a)
9.42cm
b)
150.80cm
c)
4.71cm
d)
18.85cm
21.
Find the length of the arc to 2dp
a)
31.42cm
b)
15.71cm
c)
282.74cm
d)
23.56cm
22.
Find the length of the arc to 2dp
a)
2.09m
b)
301.59m
c)
1.05m
d)
2.51m
23.
Find the length of the arc to 2dp
a)
25.12cm
b)
12.57cm
c)
628.32cm
d)
31.42cm
24.
Find the length of the arc to 2dp
a)
1.95cm
b)
3.91cm
c)
0.98cm
d)
2.93cm
25.
Find the length of the arc to 2dp
a)
49.74cm
b)
24.87cm
c)
4.97cm
d)
24.9cm
26.
Find the length of the arc to 2dp
a)
32.11cm
b)
16.05cm
c)
780.84cm
d)
32.99cm
27.
Find the length of the arc to 2dp
a)
246.09cm
b)
24.61cm
c)
123.05cm
d)
240.86cm
28.
Find the length of the arc to 2dp
a)
37.70cm
b)
37.69cm
c)
18.85cm
d)
18.84cm
29.
Find the length of the arc to 2dp
a)
43.98cm
b)
439.82cm
c)
219.91cm
d)
21.99cm
30.
Find the length of the arc to 2dp
a)
0.63cm
b)
0.62cm
c)
0.31cm
d)
6.28cm
31.
Find the length of the arc to 2dp
a)
21.99mm
b)
65.97mm
c)
32.99mm
d)
11.00mm
32.
Find the length of the arc to 2dp
a)
7.07cm
b)
14.13cm
c)
28.27cm
d)
42.41cm
33.
Find the length of the arc to 2dp
a)
115.61cm
b)
28.90cm
c)
57.81cm
d)
86.71cm
34.
Find the length of the arc to 2dp
a)
5.76cm
b)
18.85cm
c)
7.33cm
d)
11.52cm
35.
The largest cookie ever baked had an area of 8,171 ft². Which of these is the closest to the radius of the cookie?
a)
60 ft
b)
51 ft
c)
42 ft
d)
102 ft
36.
what is the area of a circle with the diameter of 10cm ?
a)
66 cm2
b)
78.5 cm2
c)
66.5 cm2
d)
10 m2
37.
A cruise ship has a large, circular window. It has an area of 50 meters. Which is closest to the window's diameter?
a)
6 m
b)
3 m
c)
8 m
d)
10.5 m
38.
Given circle P, m ∠ RPT = 130°, and PT = 18 cm.
Solve for area of the shaded sector.
a)
367.57 cm2
b)
207.23 cm2
c)
324.08 cm2
d)
182.67 cm2
39.
Given circle P, m ∠ RPT = 130°, and PT = 18 cm.
Solve for area of the shaded sector.
a)
117.94 cm2
b)
650.31 cm2
c)
324. 68 cm2
d)
210.81 cm2
40.
Given the measurements in the diagram, find the total area of the shaded regions.
a)
10.47 cm2
b)
17.45 cm2
c)
26.18 cm2
d)
8.33 cm2
41.
Find the measure of arc AB.
a)
17
b)
34
c)
68
d)
146
42.
Find the area of each sector.
a)
52.4 in2
b)
18,864 in2
c)
60 in2
d)
10.47 in
43.
FIND THE ARC LENGTH OF THE BOLDED ARC
a)
A
b)
B
c)
C
d)
D
44.
Calculate the length of an arc with radius 15 cm and central angle of 30°.
a)
450 cm
b)
5π/2 cm or ≈ 7.9 cm
c)
225 cm
d)
5π/4 cm or ≈ 3.9 cm
45.
Calculate the area of a sector with central angle of 140° and radius of 8 cm.
a)
224/9 cm2 or ≈ 24.9 cm2
b)
896 π/9 cm2 or ≈ 312.8 cm2
c)
4480 cm2
d)
224 π/ 9 cm2 or ≈ 78.2 cm2
46.
Determine the central angle if the arc length is 10 cm and the radius is 5 cm.
a)
2°
b)
not possible ... "s" is too small
c)
≈ 114.6°
d)
360°
47.
What is the radius of the circle with area of a sector equal to 7π cm2 and central angle of 70°?
a)
6 cm
b)
1π/5 cm or .6 cm
c)
.8 cm
d)
36 cm
48.
A ceiling fan with 16 inch blades rotates at 45 rpm. Find the angular velocity of the fan in rad/min. Round to the nearest tenth.
a)
90 rad/min
b)
282.7 rad/min
c)
45 rad/min
d)
141.4
49.
Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.
a)
5654.9 in/min
b)
1800 in/min
c)
2827.4 in/min
d)
900 in/min
50.
How many revolutions will a car wheel of diameter 30 in. make as the car travels a distance of one mile? (Hint: determine the circumference first ... rev/circumference ... then convert to rev/mile) Round answer to the nearest tenth.
a)
6635.0 rev/mile
b)
672.3 rev/mile
c)
884.7 rev/mile
51.
The wheels of a car have radius 11 in. and are rotating at 600 rpm. Determine the speed of the car in miles/hour to the nearest tenth. (Determine ω (angular velocity) first and then use v=ω⋅r and convert to miles/hour)
a)
6.3 miles/hour
b)
12.5 miles/hour
c)
39.3 miles/hour
d)
78.5 miles/hour
52.
Determine the angular velocity in rad/min of a gyroscope rotating at 6 rps (revolutions per second). Leave answer in terms of π.
a)
360π rad/min
b)
12π rad/min
c)
360 rad/min
d)
720π rad/min
53.
A ceiling fan with 16 inch blades rotates at 45 rpm. Find the angular velocity of the fan in rad/min. Round to the nearest tenth.
a)
90 rad/min
b)
282.7 rad/min
c)
45 rad/min
d)
141.4
54.
Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.
a)
5654.9 in/min
b)
1800 in/min
c)
2827.4 in/min
d)
900 in/min
55.
Determine the angular velocity in rad/min of a gyroscope rotating at 6 rps (revolutions per second). Leave answer in terms of π.
a)
360π rad/min
b)
12π rad/min
c)
360 rad/min
d)
720π rad/min
56.
A ceiling fan has 18 inch blades and turns at a rate of 45 revolutions per minute. What is the angular speed in radians per hour?
a)
90π rad / 1 hr
b)
2700π rad / 1 hr
c)
5400π rad / 1 hr
d)
97200π rad / 1 hr
57.
A car tire has a diameter of 14 inches and is spinning at 10 revolutions per second. What is the linear speed in miles per hour?
a)
7.95π mi / 1 hr
b)
15.90 mi / 1 hr
c)
3.28 rad / 1 hr
d)
2.84 rad / 1 hr
58.
A car tire has a diameter of 14 inches and is spinning at a rate of 10 revolutions per second. What is the angular speed in radians per hour?
a)
120π rad / 1 hr
b)
1,008,000π rad / 1 hr
c)
504,000π rad / 1 hr
d)
7200π rad / 1 hr
59.
A spin balancer rotates the wheel of a car at 500 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested?
a)
12.31π mi / 1 hr
b)
12.09π mi / 1 hr
c)
13. 44π mi / 1 hr
d)
24.62π mi / 1 hr
60.
A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed?
a)
3.2 rad/s
b)
26 rad/s
c)
52 rad/s
d)
81 rad/s
61.
Two bugs ride a turntable which is rotating at a constant rate of 4 rad/s. Bug A is at a radius of 4 cm, while bug B is at a radius of 8 cm. Which of the following is true?
a)
Bug A has a greater rotational speed.
b)
Bug B has a greater rotational speed.
c)
Bug A has a greater speed.
d)
Bug B has a greater speed.
62.
Which has greater angular speed, a horse near the outside rail of a merry-go-round or a horse near the inside rail?
a)
The inside horse
b)
The outside horse
c)
Neither - they both have the same angular speed
63.
A bug on a turning phonograph record will make more turns per minute if it is located toward the center of the record.
a)
True
b)
False
64.
A ceiling fan with 16 inch blades rotates at 45 rpm. Find the angular velocity of the fan in rad/min. Round to the nearest tenth.
a)
90 rad/min
b)
282.7 rad/min
c)
45 rad/min
d)
141.4
65.
Calculate the length of an arc with radius 15 cm and central angle of 30°.
a)
450 cm
b)
5π/2 cm or ≈ 7.9 cm
c)
225 cm
d)
5π/4 cm or ≈ 3.9 cm
66.
Calculate the area of a sector with central angle of 140° and radius of 8 cm.
a)
224/9 cm2 or ≈ 24.9 cm2
b)
896 π/9 cm2 or ≈ 312.8 cm2
c)
4480 cm2
d)
224 π/ 9 cm2 or ≈ 78.2 cm2
67.
Determine the central angle if the arc length is 10 cm and the radius is 5 cm.
a)
2°
b)
not possible ... "s" is too small
c)
≈ 114.6°
d)
360°
68.
What is the radius of the circle with area of a sector equal to 7π cm2 and central angle of 70°?
a)
6 cm
b)
1π/5 cm or .6 cm
c)
.8 cm
d)
36 cm
69.
A ceiling fan with 16 inch blades rotates at 45 rpm. Find the angular velocity of the fan in rad/min. Round to the nearest tenth.
a)
90 rad/min
b)
282.7 rad/min
c)
45 rad/min
d)
141.4
70.
Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.
a)
5654.9 in/min
b)
1800 in/min
c)
2827.4 in/min
d)
900 in/min
71.
How many revolutions will a car wheel of diameter 30 in. make as the car travels a distance of one mile? (Hint: determine the circumference first ... rev/circumference ... then convert to rev/mile) Round answer to the nearest tenth.
a)
6635.0 rev/mile
b)
672.3 rev/mile
c)
884.7 rev/mile
72.
The wheels of a car have radius 11 in. and are rotating at 600 rpm. Determine the speed of the car in miles/hour to the nearest tenth. (Determine ω (angular velocity) first and then use v=ω⋅r and convert to miles/hour)
a)
6.3 miles/hour
b)
12.5 miles/hour
c)
39.3 miles/hour
d)
78.5 miles/hour
73.
Determine the angular velocity in rad/min of a gyroscope rotating at 6 rps (revolutions per second). Leave answer in terms of π.
a)
360π rad/min
b)
12π rad/min
c)
360 rad/min
d)
720π rad/min
74.
How many radians does a circle have?
a)
360 degrees
b)
2pi radians
c)
pi radians
d)
2 radians
75.
Convert π/4 radians to degrees
a)
90⁰
b)
45⁰
c)
60⁰
d)
30⁰
76.
Convert 150⁰ to radians
a)
5π/6
b)
3π/4
c)
7π/6
d)
2π/3
77.
Convert 3π/4 to degrees
a)
147.3°
b)
135°
c)
125°
d)
173.8°
78.
Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20 inch blades rotating at 45 rpm.
a)
5654.9 in/min
b)
1800 in/min
c)
2827.4 in/min
d)
900 in/min
79.
Calculate the area of a sector with central angle of 140° and radius of 8 cm.
a)
224/9 cm2 or ≈ 24.9 cm2
b)
896 π/9 cm2 or ≈ 312.8 cm2
c)
4480 cm2
d)
224 π/ 9 cm2 or ≈ 78.2 cm2
80.
Determine the central angle if the arc length is 10 cm and the radius is 5 cm.
a)
2°
b)
not possible ... "s" is too small
c)
≈ 114.6°
d)
360°
81.
A spin balancer rotates the wheel of a car at 500 revolutions per minute. If the diameter of the wheel is 26 inches, what is the angular speed in degrees per second?
a)
16.67 deg / sec
b)
6,000 deg / 1 sec
c)
3,000 deg / 1 sec
d)
180,000 deg / 1 sec
82.
A grindstone spinning at the rate of 8.3 rev/s has what approximate angular speed?
a)
3.2 rad/s
b)
26 rad/s
c)
52 rad/s
d)
81 rad/s
83.
Two bugs ride a turntable which is rotating at a constant rate of 4 rad/s. Bug A is at a radius of 4 cm, while bug B is at a radius of 8 cm. Which of the following is true?
a)
Bug A has a greater rotational speed.
b)
Bug B has a greater rotational speed.
c)
Bug A has a greater speed.
d)
Bug B has a greater speed.
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