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Arc Length and Area of Sector

Total questions: 95

Worksheet time: 9hrs 21mins

Name
Class
Date
1.
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.
2.
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 thenearest 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
3.
Find the arc length.  Leave your answer in terms of π.
a)
7/4π
b)
7/2π
c)
1/8π
d)
45π
4.
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
5.
Find the measure of arc AB.
a)
17
b)
34
c)
68
d)
146
6.
Find the length of the bold arc.Leave pi in your answer.
a)
5688π ft
b)
15.8π ft
c)
150.4π ft
d)
54,150 ft
7.
Find the area of each sector.
a)
52.4 in2
b)
18,864 in2
c)
60 in2
d)
10.47 in
8.
If the length of the 45° region of this circle is 10 inches, what is the radius of the circle?
a)
1.6in
b)
3in
c)
6.8in
d)
2.5in
9.

Given that m∠AOB = 13π/18 and the radius is 8 cm, what is the length of arc AB?

a)

13π/8 cm

b)

52π/9 cm

c)

π/9 cm

d)

9π/52

10.

Find the area of a sector with an arc length of 30 cm and a radius of 8 cm.

a)

240 cm2

b)

80 cm2

c)

120 cm2

d)

180 cm2

11.

What is the area of sector​ GPH?

a)

9π yd2

b)

32π yd2

c)

18π yd2

d)

6π yd2

12.

Find the area of the shaded sector of the circle.

a)
b)
c)
d)
13.

In a​ circle, a 90° sector has area 64π in2. What is the radius of the​ circle?

a)

16 in

b)

32 in

c)

64 in

d)

128 in

14.
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
15.
What is the area of the shaded region? Round to the nearest hundredth.
a)
1.26
b)
452.39
c)
113.10
d)
40715.04
16.
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
17.
In the equation (x-3)2+(y-2)2=16, the center of the circle is...
a)
(3,2)
b)
(-3, -2)
c)
(-2, -3)
d)
(2, 3)
18.
In the equation (x+2)2+(y-3)2=4, the radius of the circle is...
a)
4
b)
2
c)
3
d)
16
19.

What is x?

a)

15

b)

23

c)

2

d)

92

20.
Find the arc length of arc AB.
a)
12.57 units
b)
75.40 units
c)
24 units
d)
125.66 units
21.
Stephanie was jogging around circular track. One part of the track was darker than the rest. She found the angle to be 270 degrees. She found the diameter was thirty feet. What is the arc length around the darker part of the track she jogged on? (rounded to the nearest whole number)
a)
71 feet
b)
141 feet
c)
84 feet
d)
63 feet
22.
If Pacman's mouth, when open, is 70° and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body?
a)
161.97 mm2
b)
What's Pacman?
c)
39.1 mm2
d)
9.77 mm2
23.
Find the area of the shaded sector
a)
173.42 cm2
b)
212.06 cm2
c)
237.50 cm2
d)
not enough information
24.
Find the area of the shaded sector.
a)
37.70 cm2
b)
6.28 cm2
c)
28.27 cm2
d)
9.42 cm2
25.
Find the length of the minor arc.
a)
5.24 units
b)
1.88 units
c)
2.62 units
d)
3.77 units
26.

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.

a)

0.3 square units

b)

15.7 square units

c)

19.7 square units

d)

50.3 square units

27.

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

28.
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)
90
b)
60
c)
55
d)
113
29.

If Pacman's mouth, when open, is 7π/18 radians and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body?

a)

161.97 mm2

b)

What's Pacman?

c)

39.1 mm2

d)

9.77 mm2

30.

What is the length of the arc from Tasha's dog house to the hydrant, following minor arc DG, to the nearest foot.

a)

40 ft

b)

35 ft

c)

55 ft

d)

69 ft

31.
What is the area of the shaded sector?
a)
743.61 cm2
b)
655.39 cm2
c)
163.85 cm2
d)
None of the above
32.
What is the area of the shaded sector?
a)
145.31 cm2
b)
20.76 cm2
c)
581.25 cm2
d)
470.13 cm2
33.

What is the scale factor of the two triangles?

a)

2

b)

3/2

c)

2/3

d)

1/2

34.

What is the scale factor?

a)

1/4

b)

.25

c)

5/28

d)

6

35.

Are the two objects similar?

a)

Yes

b)

No

36.

Determine if the volumes are similar, and if yes, the correct scale factor.

a)

No

b)

Yes, 1/2

c)

Yes, 1/3

d)

Yes, 2/3

37.

Given the triangles are similar and the area of the larger triangle is 100, what is the area of the smaller triangle?

a)

200 units2

b)

25 units2

c)

6.25 units2

d)

12.75 units2

38.
Tell whether the two figures are similar. Explain your reasoning. (Hint: are they proportional?)
a)
Yes, similar because they are the same shape and side lengths are proportional.
b)
No, not similar because they are the same shape, but side lengths are not proportional.
c)
Yes, same shape
d)
No, different sizes
39.

Given the rectangles are similar and the area of the smaller is 8 ft2, what is the area of the larger rectangle?

a)

200 ft2

b)

40 ft2

c)

120 ft2

40.

Given the circles are similar and the area of the larger circle is 254.5 m2, what is the area of the smaller circle?

a)

141.4 m2

b)

78.5 m2

c)

824.6 m2

d)

458.1 m2

41.

Given the pentagons are similar, and the area of the larger is 440.4 in2, what is the area of the smaller pentagon?

a)

587.2 in2

b)

330.3 in2

c)

782.9 in2

d)

247.73 in2

42.
Are the two figures similar?
(If yes, what is the similarity ratio?)
a)
Yes; 3
b)
Yes; 3/10
c)
Yes; 3/5
d)
No
43.
Are the two figures similar?
(If yes, what is the similarity ratio?)
a)
Yes; 5
b)
Yes; 9:6
c)
Yes; 1/3
d)
No
44.

Determine if the volumes are similar, and if yes, the correct scale factor.

a)

Yes, 1/2

b)

No

c)

Yes, 1/4

45.

What is the scale factor of the two cylinders?

a)

3/8

b)

3/4

c)

2/4

d)

6/8

46.

Given the cylinders are similar and the volume of the larger is 804.25 m3, what is the smaller volume?

a)

339.3 m3

b)

1,906.4 m3

c)

452.4 m3

d)

603.2 m3

47.

The volume of the larger cone is 22.6 mi3, what is the smaller cone volume?

a)

5.65 mi3

b)

11.3 mi3

c)

2.83 mi3

d)

180.8 mi3

48.

The pyramids are similar. Find the volume of the red pyramid.

a)

21.3 in3

b)

3.8 in3

c)

12 in3

d)

16 in3

49.
What is the coordinates of the centre and the radius of the circle with equation:
(x - 4)2 + (y - 3)2 = 25 ?
a)
Centre  (4,3)
Radius = 5 units
b)
Centre  (4,3)
Radius = 25 units
c)
Centre  (-4,-3)
Radius = 25 units
d)
Centre  (-4,-3)
Radius = 5 units
50.
What is the coordinates of the centre and the radius of the circle with equation:
(x + 7)2 + (y - 6)2 = 64 ?
a)
Centre (7,-6)
Radius = 8 units
b)
Centre (-7,6)
Radius = 64 units
c)
Centre (-7,6)
Radius = 8 units
d)
Centre (7,-6)
Radius = 64 units
51.
What is the equation of the circle, with centre (4,2) and radius 5 units?
a)
(x + 4)2 + (y + 2)2 = 25
b)
(x + 4)2 + (y + 2)2 = 5
c)
(x - 4)2 + (y - 2)2 = 5
d)
(x - 4)2 + (y - 2)2 = 25
52.
What is the equation of the circle, with centre (-2,-7) and radius 3 units?
a)
(x + 2)2 + (y + 7)2 = 3
b)
(x - 2)2 + (y - 7)2 = 9
c)
(x + 2)2 + (y + 7)2 = 9
d)
(x - 2)2 + (y - 7)2 = 3
53.
What is the equation of the circle, with centre (-4,5) and radius 6 units?
a)
(x - 4)2 + (y + 5)2 = 6
b)
(x - 4)2 + (y + 5)2 = 36
c)
(x + 4)2 + (y - 5)2 = 6
d)
(x + 4)2 + (y - 5)2 = 36
54.
a)

(x+1)2 + (y +1)2 = 3

b)

(x+1)2 + (y -1)2 = 3

c)

(x-1)2 + (y -1)2 = 9

d)

(x+1)2 + (y +1)2 = 9

55.
The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.
a)
(x - 2)2 + (y + 5)2 = 36
b)
(x - 5)2 + (y + 2)2 = 6
c)
(x + 5)2 + (y - 2)2 = 36
d)
(x + 2)2 + (y - 5)2 = 6
56.

What are the coordinates of the center and the radius of the circle with equation:

x2 + y2 - 8x - 6y = -9 ?

a)

Center (4,3)

Radius = 4 units

b)

Center (4,3)

Radius = 25 units

c)

Center (-4,-3)

Radius = 25 units

d)

Center (-4,-3)

Radius = 5 units

57.
What is the equation of the circle?
a)
(x+1)2 + (y +1)2 = 3
b)
(x+1)2 + (y -1)2 = 3
c)
(x+1)2 + (y +1)2 = 9
d)
(x-1)2 + (y -1)2 = 9
58.

Determine the center and radius of x2+ y2-10x+6y +9 = 0

a)

(5,-3) and 25

b)

(-5,3) and 25

c)

(-5,-3) and 5

d)

(5,-3) and 5

59.

The point (-5,6) is on a circle with center (-1,3) write the equation of the circle

a)

(x+1)2 + (y-3)2= 4000

b)

(x+5)2 + (y-0)2= 25

c)

(x+1)2 + (y-3)2= 25

d)

(x-1)2 + (y+3)2= 25

60.
Find the center if the endpoints of the diameter are at (-12, -7) and (3, 5).
a)
(-4.5, -1)
b)
(-7.5, -6)
c)
(4.5, 1)
d)
(7.5, 6)
61.

What is the equation for the circle, if it has diameter endpoints at (3,-4) and (-5,-4)?

a)

(x+1)² + (y-4)² = 4

b)

(x+1)² + (y+4)² = 16

c)

(x-1)² + (y-4)² = 16

d)

(x+1)² + (y+4)² = 4

62.
What is the equation of this circle?
a)
(x + 3)2 + (y - 1)2 = 9
b)
(x - 3)2 + (y + 1)2 = 9
c)
(x - 3)2 + (y + 1)2 = 3
d)
(x + 3)2 + (y - 1)2 = 3
63.
a)

(x+1)2+(y-5)2=128

b)

(x-1)2+(y+5)2=11.31

c)

(x-1)2+(y+5)2=128

d)

(x+1)2+(y+5)2=11.31

64.

The point (-5,4) is on a circle with center (3,-2). Write the equation of the circle.

a)

(x+5)2+(y-4)2=10

b)

(x-3)2+(y+2)2=100

c)

(x-5)2+(y+4)2=10

d)

(x-5)2+(y+4)2=100

65.
What is the radius of the given circle:
 x²+y²-10x+8y-23=0?
a)
4
b)
2
c)
8
66.
Determine the center and radius: x2 + y2 + 14x - 2y = -1
a)
center= (-7,2) radius= 3
b)
center= (-7,1) radius= 7
c)
center= (-4,1) radius= 5
67.

Determine the equation of the circle in standard form:

x2 + y2 + 6x - 12y + 20 = 0

a)

(x-3)2 + (y+6)2 = 25

b)

(x+3)2 + (y-6)2 = 25

c)

(x-3)2 + (y+6)2 = 45

d)

(x+3)2 + (y-6)2 = 5

68.
Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0
a)
(x+2)2 + (y+3)2 = 49
b)
(x+2)2 + (y+3)2 = 13
c)
(x-2)2 + (y-3)2 = 49
d)
(x-2)2 + (y-3)2 = 13
69.
What is the equation of the circle, with centre (-4,5) and radius 6 units?
a)
(x - 4)2 + (y + 5)2 = 6
b)
(x - 4)2 + (y + 5)2 = 36
c)
(x + 4)2 + (y - 5)2 = 6
d)
(x + 4)2 + (y - 5)2 = 36
70.
a)

A

b)

B

c)

C

d)

D

71.
What is the value of x?
a)
92
b)
25
c)
12.5
d)
105
72.
Find the m∠ABD.
a)
14
b)
51
c)
37
d)
65
73.
Find the measure of arc KM.
a)
29
b)
33
c)
41.5
d)
50
74.
Solve for x.
a)
x = 35.67
b)
x = -1
c)
x = 14
d)
x = -4.33
75.
Find the value of x.
a)
x = 17
b)
x = 16
c)
x = 29.67
d)
x = 18
76.
In the circle, find the measure of angle CAB.
a)
A
b)
B
c)
C
d)
D
77.
What is the measure of angle 2?
a)
80
b)
45
c)
125
d)
40
78.
What is the measure of angle 1?
a)
130
b)
65
c)
44
d)
86
79.
Solve for x.
a)
29
b)
33
c)
41.5
d)
50
80.

Determine the value of z.

a)

37.5

b)

55

c)

57.5

d)

75

81.
Find the measure of angle MNQ.
a)
89
b)
45
c)
158
d)
22
82.

Solve for m∠TSR.

a)

250°

b)

70°

c)

80°

83.
Solve for the missing angle.
a)
24o
b)
48o
c)
12o
d)
6o
84.
What is the measure of angle 1?
a)
120
b)
40
c)
30
d)
60
85.
Find the measure of arc AB.
a)
17
b)
34
c)
68
d)
146
86.
Determine the value of all three variables. Rank a, b, and c in order from greatest to least.
a)
a,b,c
b)
b,a,c
c)
c,a,b
d)
c,b,a
87.
What is the value of y?
a)
27
b)
54
c)
108
d)
540
88.
Solve for a.
a)
6
b)
6.67
c)
8.33
d)
10
89.
Solve for a.
a)
4
b)
6.93
c)
8
d)
16
90.
Solve for
a)
9
b)
10
c)
15
d)
14
91.
Solve for x. 
a)
7.94
b)
8
c)
10.58
d)
112
92.
Solve for x.
a)
6
b)
7.94
c)
8
d)
9
93.
Solve for x.
a)
6
b)
8
c)
10
d)
12
94.
What is the value of x?
a)
18
b)
8
c)
10
d)
30
95.
A tangent to a circle is ________________________ to the radius drawn to the point of tangency.
a)
congruent
b)
perpendicular
c)
complimentary
d)
supplementary

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