Free Printable Conversion Radians/Degrees, Arc Length, & Sector Area Review

1.

Which is the correct conversion factor to use when converting from DEGREES TO RADIANS?

a)

180^o/π rad

b)

π rad / 180^o

c)

π rad / 360^o

d)

^360o/π rad

2.

Which is the correct conversion factor to use when converting from RADIANS TO DEGREES?

a)

180^o/π rad

b)

π rad / 180^o

c)

π rad / 360^o

d)

^360o/π rad

3.

What is $\frac{2\pi}{3}$ radians in degrees?

a)

$150\degree$

b)

$120\degree$

c)

$180\degree$

d)

$30\degree$

4.

What is $225\degree$ in radians?

a)

$\frac{7\pi}{4}$

b)

$\frac{5\pi}{4}$

c)

$\frac{3\pi}{4}$

d)

$\frac{5\pi}{3}$

5.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

6.

Find the arc length.

a)

3π/4 ft

b)

39π/4 ft

c)

13π/4 ft

d)

4π/13 ft

7.

If the length of the 45° region of this circle is 10 inches, what is the radius of the circle?

Round to the nearest tenth.

a)

0.2 in

b)

12.7 in

c)

25.5 in

d)

6.4 in

8.

Circle Z has an arc length of $\frac{32\pi}{15}$ cm and a central angle YZX of 64 degrees.

Solve for the length of the radius.

a)

6 cm

b)

12 cm

c)

7 cm

d)

14 cm

9.

What is the area of the shaded sector?

a)

221π/36

b)

3757π/72

c)

3757π/18

d)

None of these

10.

Find the sector area.

a)

$114\pi$

b)

$147\pi$

c)

$234\pi$

d)

$125\pi$

11.

What is $270\degree$ in radians?

a)

$\frac{\pi}{4}$

b)

$\frac{3\pi}{2}$

c)

$\frac{3\pi}{4}$

d)

$\frac{\pi}{2}$

12.

What is $\frac{7\pi}{4}$ in degrees?

a)

$300\degree$

b)

$135\degree$

c)

$315\degree$

d)

$45\degree$

13.

Convert 150⁰ to radians

a)

$\frac{5\pi}{6}$

b)

$\frac{3\pi}{4}$

c)

$\frac{7\pi}{6}$

d)

$\frac{2\pi}{3}$

14.

$\frac{8\pi}{3}$ is equivalent to what degree measure?

a)

$480\degree$

b)

$240\degree$

c)

$800\degree$

d)

$24\degree$

15.

Convert 510^o to Radians

a)

25π / 3

b)

23π / 8

c)

17π / 6

d)

51π / 8

16.

a)

x = 160

b)

x = 80

17.

What is the measure of ∠PTQ?

a)

100°

b)

140°

18.

Find the arc length of the bolded arc. Give your answer in terms of π.

a)

(65/12)π cm

b)

17.02 cm

c)

(845/24)π cm

d)

26π cm

19.

Find arc length

a)

114π/5 ft

b)

2850 ft

c)

95π/6 ft

d)

150π/19 ft

20.

The length of an arc is 18cm and the radius of the circle is 6cm. What is the radian measure of the central angle?

a)

3 radian

b)

2 radian

c)

4 radian

d)

2π radian

21.

Find the arc length

a)

7 cm

b)

28π cm

c)

7π cm

d)

28 cm

22.

Find the arc length

a)

12π cm

b)

15π cm

c)

39.375 cm

d)

14π cm

23.

Find the arc length indicated by the bolded arc.

a)

8.3 in

b)

7.2 in

c)

6.8 in

d)

6.4 in

24.

Find the arc length indicated by the bolded arc.

a)

31.4 cm

b)

354.0 cm

c)

706.9 cm

d)

442.4 cm

25.

Find the arc length indicated by the bolded arc.

a)

75.7 in

b)

84.2 in

c)

55.6 in

d)

22.3 in

26.

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. (Use 3.14 for $\pi$ )

a)

90

b)

60

c)

55

d)

113

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. (Use 3.14 for $\pi$ )

a)

47

b)

74

c)

94

d)

123

28.

Circle Z has an arc length of $\frac{1513\pi}{180}$ km and a central angle YZX of 89^o.

Solve for the length of the radius.

a)

17 km

b)

8.5 km

c)

19 km

d)

8.5 km

29.

Circle Z has an arc length of $28\pi$ km and a central angle YZX of $\frac{2\pi}{3}$ radians.

Solve for the length of the radius.

a)

42 km

b)

21 km

c)

13 km

d)

26 km

30.

Circle Z has an arc length of $\frac{28\pi}{9}$ km and a central angle YZX of $\frac{4\pi}{9}$ rad.

Solve for the length of the radius.

a)

7 km

b)

14 km

c)

16 km

d)

8 km

31.

A sector of Circle Z has an arc length of 17 $\pi$ km and a radius of 3km.

Solve for the measure of the central angle in that sector.

Round to the nearest thousandth.

a)

17.802 rad

b)

17.803 rad

c)

0.554 rad

d)

0.555 rad

32.

A sector of Circle Z has an arc length of 72 km and a radius of 15km.

Solve for the measure of the central angle in that sector.

a)

$\frac{24}{5}$ rad

b)

$\frac{25}{4}$ rad

c)

$\frac{42}{5}$ rad

d)

$\frac{45}{2}$ rad

33.

A sector of Circle Z has an arc length of 3 km and a radius of 17𝛑km.

Solve for the measure of the central angle in that sector.

Round to the nearest thousandth.

a)

199.584^o

b)

10.111^o

c)

3.218^o

d)

99.792^o

34.

Solve for the missing angle. Write your answer as just a number. No "degrees."

(a)

35.

Solve for x.

a)

5

b)

20

c)

40

d)

85

36.

Solve for x.

a)

x = 6.45

b)

x = 8

c)

x = 12.6

d)

x = 7

37.

What is the ϴ called?

a)

sector

b)

segment

c)

arc

d)

central angle

38.

What is the length L called?

a)

circumference

b)

tangent

c)

arc

d)

sector

39.

What is the green area called?

a)

sector

b)

segment

c)

arc

d)

section

40.

Match the following formulas.

a)

$\ 2\pi\left(r\right)$

1.

Circumference

b)

$\ \pi\left(r\right)^2$

2.

Area

c)

$\ \frac{2\pi\left(r\right)\left(\theta\right)}{360\degree}$

3.

Arc Length

d)

$\ \frac{\pi\left(r\right)^2\left(\theta\right)}{360\degree}$

4.

Area of Sector

41.

Match the following

a)

The distance around the circle.

1.

Circumference

b)

The amount of space inside the circle.

2.

Area

c)

The distance around a section of the circle.

3.

Arc Length

d)

The amount of space inside a section of the circle.

4.

Area of a Sector

42.

If Pacman's mouth is open to 70° and the radius of his mouth is 8mm, what is CENTRAL ANGLE MEASURE of his Body?

a)

290^o

b)

270^o

c)

180^o

d)

110^o

43.

If Pacman's mouth is open to 70° and the radius of his mouth is 8mm, what is the sector area of his Body?

a)

$\frac{464\pi}{9}$ mm²

b)

$\frac{448\pi}{29}$ mm²

c)

$\frac{29\pi}{2304}$ mm²

d)

$\frac{112\pi}{9}$ mm²

44.

FIND THE SECTOR AREA OUTLINED IN BOLD

a)

A

b)

B

c)

C

d)

D

45.

Find the area of each sector.

a)

4248 m²

b)

7.9 m²

c)

2827.4 m²

d)

11.8 m²

46.

FIND THE SECTOR AREA OUTLINED IN BOLD

a)

A

b)

B

c)

C

d)

D

47.

Find the area of the blue shaded sector.

a)

37.70 cm²

b)

6.28 cm²

c)

28.27 cm²

d)

9.42 cm²

48.

In a circle with a diameter of 32 mi, the area of a sector is $\frac{512\pi}{3}$ mi².
The measure of the angle in the sector is ___.

a)

$\frac{\pi}{3}$ rad

b)

$\frac{4\pi}{3}$ rad

c)

$\frac{16\pi}{3}$ rad

d)

$\frac{64\pi}{3}$ rad

49.

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

a)

15.4m²

b)

15.3m²

c)

15.5m²

d)

15.6cm²

50.

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

51.

Find the sector area of the blue piece.

a)

10.598 m²

b)

2.355 m²

c)

4.710 m²

d)

7.684 m²

52.

In circle O, the length of radius is 9 centimeters and the area of sector AOB is $\frac{27\pi}{2}$ square centimeters. The measure of in radians is

a)

$\frac{\pi}{3}$

b)

$3\pi$

c)

$\frac{1}{3\pi}$

d)

$\frac{3}{\pi}$

Conversion Radians/Degrees, Arc Length, & Sector Area Review

Total questions: 52

Worksheet time: 1hrs 13mins

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