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Practice Degree to Radian and Radian to Degrees Arc Length

Total questions: 22

Worksheet time: 32mins

Name
Class
Date
1.

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

2.

A central angle measure 4.5 radians and has an arc of 35 inches. What is the radius of the circle?

a)

7.78 inches

b)

8.21 inches

c)

157.5 inches

d)

7 inches

3.
a)

12π cm

b)

27π cm

c)

12 cm

d)

27 cm

4.

A circle has radius 12 inches. A central angle intercepts an arc of length 36 inches. What is the radian measure of the central angle?

a)

3 radian

b)

2 radian

c)

6 radian

d)

9 radian

5.

Find the arc length.

a)

3π/4 ft

b)

39π/4 ft

c)

13π/4 ft

d)

4π/13 ft

6.

Find the arc length

a)

7 cm

b)

28π cm

c)

7π cm

d)

28 cm

7.

Find the arc length

a)

12π cm

b)

15π cm

c)

39.375 cm

d)

14π cm

8.

Find arc length

a)

114π/5 ft

b)

2850 ft

c)

95π/6 ft

d)

150π/19 ft

9.

The diameter of a circle is 8 centimeters. A central angle of the circle intercepts an arc of 12 centimeters. What is the radian measure of the angle?

a)

3

b)

4

c)

d)

3/2

10.

What is the approximate length of the arc subtended by an angle of 4π/3 radians on a circle with a radius of 6.00 meters?

a)

12.57 meters

b)

14.14 meters

c)

25.13 meters

d)

28.27 meters

11.
How many radians does a circle have?
a)
  360 degrees
b)
2pi radians
c)
pi radians
d)
2 radians
12.
Convert π radians to degrees.
a)
90⁰
b)
180⁰
c)
360⁰
d)
60⁰
13.
Convert 150⁰ to radians
a)
5π/6
b)
3π/4
c)
7π/6
d)
2π/3
14.
Convert π/3 radians to degrees
a)
60⁰
b)
30⁰
c)
90⁰
d)
45⁰
15.
Convert π/4 radians to degrees
a)
90⁰
b)
45⁰
c)
60⁰
d)
30⁰
16.
Convert 100⁰ to radians
a)
5π/9
b)
π/2
c)
5π/8
d)
5π/6
17.
What is 7π/4 radians in degrees?
a)
300
b)
135
c)
315
d)
45
18.
What is 4π/3 radians in degrees?
 
a)
120
b)
240
c)
210
d)
270
19.
What is 270 degrees in radians? 
a)
π/4
b)
3π/2
c)
3π/4
d)
π/2
20.
What is 225  degrees in radians? 
a)
7π/4
b)
5π/4
c)
3π/4
d)
5π/3
21.
What is 2π/3 radians in degrees? 
a)
150
b)
120
c)
180
d)
 30
22.
What is 11π/6 radians in degrees? 
a)
30
b)
330
c)
360
d)
 300