Free Printable Arcs, Sectors & Equations Retake

1.

Find the length of the arc in the diagram. ROUND your final answer to 2 decimal places.

Arc length = (a) cm

2.

A circle has a diameter of 15 in.

Find the circumference of the circle. Write your answer in terms of pi (For example: 10pi, 20pi, etc.)

Circumference = (a) inches

3.

A circle has a diameter of 15 in.

Find the EXACT length of the arc corresponding to a sector with a central angle of $150\degree.$

Arc Length = ______ inches

a)

$\frac{\pi}{10}$

b)

$36\pi$

c)

$\frac{25\pi}{4}$

d)

$\frac{15\pi}{2}$

4.

Find the Area of the arc in the diagram. You may ROUND your final answer to 2 decimal places.

Area = (a) $cm^2$

5.

Find the area of the sector shown in the picture.

$r=10\ units$ and the central angle measures $18\degree$ . Write your answer in terms of pi (Ex: 10 pi, 20 pi, etc.)

Sector Area = (a)

units\ ^2

6.

A sector has an area of $35\ feet^2$ . The central angle of the sector is $40\degree.$

Find the area of the ENTIRE circle.

Area = (a)

feet^2

7.

The length of an arc with central angle $90\degree$ is $10\pi$ cm. What is the RADIUS of the circle?

a)

40 cm

b)

20 cm

c)

10 cm

d)

5 cm

8.

What is the length of the blue arc?

a)

45⁰

b)

3.9 mi

c)

5.9 mi

d)

7.9 mi

9.

What is the length of the green arc?

a)

1.6 mi

b)

6.3 mi

c)

3.1 mi

d)

12.6 mi

10.

What is the length of the blue arc?

a)

42.4 in

b)

1.2 in

c)

95.4 in

d)

21.2 in

11.

What is the area of the blue shaded sector?

a)

18.9 cm²

b)

56.5 cm²

c)

113.1 cm²

d)

14.1 cm²

12.

What is the are of the blue shaded sector?

a)

19.6 m²

b)

3.9 m²

c)

7.9 m²

d)

78.5 m

13.

What is the area of the yellow shaded sector?

a)

23.6 m²

b)

11.8 m²

c)

62.8 m²

d)

117.8 m²

14.

What is the area of the green shaded segment?

a)

18.3 cm²

b)

50.3 cm²

c)

169.1 cm²

d)

201.1 cm²

15.

What is the area of the green shaded segment?

a)

4.2 cm²

b)

0.2 cm²

c)

4.0 cm²

d)

2.4 cm

16.

What is the area of the blue shaded sector?

a)

11.5 cm²

b)

7.3 cm²

c)

22.9 cm²

d)

8.5 cm²

17.

What is the area of the pink shaded sector?

a)

12.6 u²

b)

4.2 u²

c)

73.0 u²

d)

113.0 u²

18.

What is the area of the blue shaded sector?

a)

38.3 yd²

b)

84.5 yd²

c)

26.7 yd²

d)

120.2 yd

19.

What is the area of the pink shaded segment?

a)

10.6 m²

b)

13.8 m²

c)

30.7 m²

d)

41.3 m²

20.

What region of a circle is defined as the region bounded by two radii and their intercepted arc.

a)

sector

b)

segment

c)

arc

d)

angle

21.

What is the region of a circle that is the part bounded by an arc and the segment joining the endpoints.

a)

sector

b)

segment

c)

arc

d)

angle

22.

What is defined as the product of the ratio of the measure of the arc divided by 360 and the circumference of the circle?

a)

arc measure

b)

sector area

c)

segment area

d)

arc length

23.

What fraction of the circle does minor arc AB represent?

a)

82/180

b)

41/180

c)

180/82

d)

180/41

24.

What fraction of the circle does major arc ACB represent?

a)

278/180

b)

180/278

c)

180/139

d)

139/180

25.

How does the process for finding the arc length differ from the process for finding the sector area?

a)

The arc length is a degree while the sector area is labeled in square units.

b)

The arc length uses π while the sector area does not always use π.

c)

The arc length and sector area are always equal.

d)

The arc length requires using the circumference while sector area requires the circle area formula.

26.

Which of the following equations cannot be used to find the circumference of a circle?

a)

C=πd

b)

C=2πr

c)

C=πr²

d)

C=dπ

27.

How many degrees (to the nearest degree) does the shaded sector's intercepted arc contain?

a)

7⁰

b)

14⁰

c)

26⁰

d)

51⁰

28.

a)

A

b)

B

c)

C

d)

D

29.

a)

A

b)

B

c)

C

d)

D

30.

a)

A

b)

B

c)

C

d)

D

31.

a)

A

b)

B

c)

C

d)

D

32.

a)

A

b)

B

c)

C

d)

D

33.

a)

A

b)

B

c)

C

d)

D

34.

a)

A

b)

B

c)

C

d)

D

35.

a)

A

b)

B

c)

C

d)

D

36.

a)

A

b)

B

c)

C

d)

D

37.

a)

A

b)

B

c)

C

d)

D

38.

What is the circumference of this circle with a diameter of 12cm?

a)

3.14 cm

b)

37.7 cm

c)

24 cm

d)

68.4 cm

39.

Find the circumference of a circle with a radius of 12.5 mm.

a)

37.68mm

b)

18.84mm

c)

78.54mm

d)

none of the above

40.

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

41.

Find the length of the arc.

a)

31.42cm

b)

15.71cm

c)

282.74cm

d)

23.56cm

42.

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

43.

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.

44.

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

45.

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

46.

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

47.

Find the circumference of the circle

a)

87.82

b)

153.86

c)

43.96

d)

307.72

48.

What is the area of this circle?

a)

8322.13

b)

1134.11

c)

4536.46

d)

1267.09

49.

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

50.

A clock face has a diameter of 10 inches. What is the approximate area of the clock face in square inches?

a)

314 in²

b)

31.4 in²

c)

7.85 in²

d)

78.5 in²

51.

what is the area of this semicircle with a diameter of 8 cm?

a)

100.48cm²

b)

80cm²

c)

200.96cm²

d)

none of the above

52.

A circle has an circumference of 56.52 cm. Find the area of the circle.

a)

1017.36 cm²

b)

254.34 cm²

c)

3194.51 cm²

d)

798.63 cm²

53.

Find the arc length of AB. Round your answer to the nearest tenth.

a)

8 units

b)

4.2 units

c)

8.4 units

d)

16.8 units

54.

Find the area of the sector. Round your answer to the nearest tenth.

a)

5.2 units²

b)

10.5 units²

c)

31.4 units²

d)

38.2 units²

55.

Find the area of the sector. Round your answer to the nearest tenth.

a)

52.4 in²

b)

5.2 in²

c)

60.8 in²

d)

10.47 in²

56.

Find the area of the sector. Round your answer to the nearest tenth.

a)

3.9 m²

b)

7.9 m²

c)

9.6 m²

d)

11.8 m²

57.

Is the formula for

a)

arc length

b)

area of a sector

c)

area of a segment

d)

arc measure

58.

Find the arc length of the sector. Round your answer to the nearest tenth.

a)

4.8 units

b)

2.6 units

c)

7.9 units

d)

5.2 units

59.

Find the arc length of the sector. Round your answer to the nearest tenth.

a)

52.4 in

b)

10.5 in

c)

5.2 in

d)

9.8 in

60.

Find the arc length of the sector. Round your answer to the nearest tenth.

a)

8.7 m

b)

7.9 m

c)

3.9 m

d)

11.8 m

61.

Find the arc length of the sector.

a)

A

b)

B

c)

C

d)

D

62.

Find the arc length of the sector.

a)

A

b)

B

c)

C

d)

D

63.

Find the area of the sector. Round your answer to the nearest tenth.

a)

3.1 yd²

b)

28.3 yd²

c)

6.3 yd²

d)

32.4 yd²

64.

Find the area of the shaded region. Round your answer to the nearest tenth.

a)

18.8 units²

b)

9.4 units²

c)

113.1 units²

d)

77.6 units²

65.

Find the arc length of the sector. Round your answer to the nearest tenth.

a)

18.8 cm

b)

56.5 cm

c)

9.4 cm

d)

32.9 cm

66.

Find the area of the sector. Round your answer to the nearest tenth.

a)

58.9 m²

b)

11.8 m²

c)

23.6 m²

d)

117.8 m²

67.

Find the area of the sector. Round your answer to the nearest tenth.

a)

12.6 units²

b)

4.2 units²

c)

6.3 units²

d)

2.1 units²

68.

Find the area of the sector. Round your answer to the nearest tenth.

a)

53.4 yd²

b)

120.2 yd²

c)

26.7 yd²

d)

13.4 yd

69.

How does the process for finding the arc length differ from the process for finding the sector area?

a)

The arc length is a degree while the sector area is labeled in square units.

b)

The arc length uses π while the sector area does not always use π.

c)

The arc length and sector area are always equal.

d)

The arc length requires using the circumference while sector area requires the circle area formula.

70.

Is the formula for

a)

arc length

b)

area of a sector

c)

area of a segment

d)

arc measure

71.

Write 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

72.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

73.

In the equation (x-4)²+(x-3)²=25, the radius is

a)

4

b)

3

c)

5

d)

25

74.

A line segment between two points on the circle which passes through the center

a)

Radius

b)

Diameter

c)

Chord

d)

Tangent

75.

Circles with exactly the same radius measures

a)

Similar Circles

b)

Concentric Circles

c)

Congruent Circles

d)

Semicircle

76.

The distance around a circle

a)

Diameter

b)

Radius

c)

Circumference

d)

Area

77.

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)

78.

Write the equation of a circle with center
(7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

79.

What is the radius of the circle
(x+7)²+(y-2)²=144?

a)

7

b)

12

c)

13

80.

What is the center of the circle with this equation is (x+2)²+(y-4)²=41?

a)

(2,-5)

b)

(-2,4)

c)

(2,-4)

d)

(-2, -4)

81.

What is the equation for this circle?

a)

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

b)

x²+y²=9

c)

x+y=9

82.

What is the radius of the circle with this equation of (x-5)²+(y+7)²=8?

a)

4

b)

8

c)

4√2

d)

2√2

83.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

84.

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)
Radius = 5 units

b)

Center (4,3)
Radius = 25 units

c)

Center (-4,-3)
Radius = 25 units

d)

Center (-4,-3)
Radius = 5 units

85.

What is the center of the circle with equation x² + y² = 1?

a)

(1, 1)

b)

(0, 0)

c)

not enough information

d)

(-1, -1)

86.

What is the center and radius for a circle with the equation:
(x-4)²+(y+2)²=25

a)

C:(4, -2), r=5

b)

C:(-4, 2), r=5

c)

C:(4, -2), r=25

d)

C:(-4, 2), r=25

87.

What is the formula for circumference of a circle given the diameter?

a)

C = pi x radius

b)

C = pi x 2radius

c)

C = pi x diameter

d)

C = pi x 2diameter

88.

What is the formula for circumference of a circle given the radius?

a)

C = pi x radius

b)

C = pi x 2radius

c)

C = pi x diameter

d)

C = pi x 2diameter

89.

What does "circumference" mean?

a)

Space a circle takes up

b)

Distance around a circle

c)

Line from one side of a circle to another

d)

Line from center of circle to side

90.

Which graph corresponds to
(x)²+ (y-6)²=9

a)

A

b)

B

c)

C

d)

D

91.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

92.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

93.

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)

94.

a)

A

b)

B

c)

C

d)

D

95.

What is the equation for this circle?

a)

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

b)

x²+y²=9

c)

x+y=9

96.

What is the center and radius in this image?

a)

C(-7,3) ; r=3

b)

C(7,-3) ; r=3

c)

C(7,-3) ; r=9

d)

C(-7,3) ; r=9

97.

What is the correct graph for the equation x²+y²=4?

a)

b)

c)

Answer is in none of the given

d)

98.

What is the diameter?

a)

8

b)

16

c)

10

d)

4

99.

What is the radius?

a)

18

b)

72

c)

38

d)

14

100.

Does the point (4,5) lie on the circle whose center is (-2,-2) and radius 9?

a)

yes

b)

No

101.

Is the point (3 , 5) inside, outside or on the circle with equation x² + y² = 9?

a)

Inside the Circle

b)

Outside the Circle

c)

On the Circle

102.

Is the point (-3 , 5) inside, outside or on the circle with equation (x+2)² + (y-4)² = 9?

a)

Inside the Circle

b)

Outside the Circle

c)

On the Circle

103.

Circle O has a center at (3,1) and a diameter of 10 units. Which point lies on circle O?

a)

(3,-4)

b)

(-3,-1)

c)

(5,1)

d)

(8,0)

104.

Write the equation of a circle with center (h,k) and radius r.

a)

x² + y² = r²

b)

(x + h)² + (y + h)² = r²

c)

(x - h)² + (y - k)² = r²

d)

(x - h)² - (h - k)² = r

105.

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

106.

Write the equation at the origin with radius 6.

a)

x² + y² = 6

b)

x² + y² = 36

c)

x + y = 6

d)

x + y = 36

107.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

108.

What is the center of a circle with equation (x-4)² + y² = 5?

a)

(-4, 0)

b)

(4, 0)

c)

(4, 1)

d)

(-4, 1)

109.

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

110.

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)

111.

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

112.

What is the radius of the circle with this equation of (x-5)²+(y+7)²=8?

a)

4

b)

8

c)

4√2

d)

2√2

113.

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

114.

What is the center of the circle $x^2+y^2=49$ ?

a)

0

b)

(0,0)

c)

49

d)

7

115.

What is the radius of the circle $x^2+\left(y-2\right)^2=16$ ?

a)

0

b)

(0,2)

c)

4

d)

256

116.

What is the center of the circle $\left(x+3\right)^2+\left(y-5\right)^2=6^2$ ?

a)

(-3,5)

b)

(3,-5)

c)

6

d)

36

117.

What is the radius of the circle $\left(x+3\right)^2+\left(y-5\right)^2=6^2$ ?

a)

(-3,5)

b)

(3,-5)

c)

6

d)

36

118.

What is the center of circle $x^2+y^2-4x+6y-36=0$ ?

a)

(-4,6)

b)

(-2,3)

c)

(2,-3)

d)

(4,-6)

119.

What is the radius of circle $x^2+y^2-4x+6y-36=0$ ?

a)

6

b)

(-2,3)

c)

(2,-3)

d)

7

120.

What is the center of circle $x^2+y^2+6x-4y-36=0$ ?

a)

(-6,4)

b)

(-3,2)

c)

(3,-2)

d)

(6,-4)

121.

What is the equation of the circle with radius $r=5$ and center $C\left(-2,3\right)$ ?

a)

$\left(x-2\right)^2+\left(y+3\right)^2=25$

b)

$\left(x+2\right)^2+\left(y-3\right)^2=5$

c)

$\left(x-2\right)^2+\left(y+3\right)^2=5$

d)

$\left(x+2\right)^2+\left(y-3\right)^2=25$

122.

What is the equation of the circle with radius $r=4$ and center $C\left(-5,2\right)$ ?

a)

$\left(x+5\right)^2+\left(y-2\right)^2=4$

b)

$\left(x+5\right)^2+\left(y-2\right)^2=4^2$

c)

$\left(x+5\right)^2+\left(y-2\right)^2=4$

d)

$\left(x-5\right)^2+\left(y+2\right)^2=16$

123.

What is the center of the circle $x^2+\left(y-2\right)^2=16$ ?

a)

0

b)

(0,-2)

c)

(0,2)

d)

4

Arcs, Sectors & Equations Retake

Total questions: 123

Worksheet time: 14hrs 27mins

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