Radians and Arc Length Worksheet
Explore radians as a unit of angle measurement and calculate arc length in circles with this Grade 11 mathematics worksheet.
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Radians and Arc Length
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. What is the radian measure equivalent to an angle of 270 degrees?
π/2 radians
3π/2 radians
2π radians
π radians
2. The formula for arc length 's' in a circle with radius 'r' and central angle 'θ' (in radians) is:
s = r + θ
s = r - θ
s = rθ
s = r/θ
3. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the of the circle.
4. To convert degrees to radians, you multiply the degree measure by .
5. A circle has a radius of 6 cm. Find the length of the arc subtended by a central angle of π/3 radians. Show your work.
6. An arc of a circle is 10 cm long and subtends a central angle of 2 radians. What is the radius of the circle? Show your work.
7. A full circle measures 360 degrees, which is equivalent to π radians.
True
False
Match the degree measure with its equivalent radian measure.
8. 45 degrees
a. π/6
9. 60 degrees
b. π/4
10. 30 degrees
c. π/3