Radians and Arc Length Worksheet

Radians and Arc Length

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. 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.

2. To convert degrees to radians, you multiply the degree measure by  .

3. The formula for arc length (s) is s = rθ, where r is the radius and θ is the angle in  .

4. Convert 150° to radians. Express your answer in terms of π.

5. Convert (3π/4) radians to degrees.

6. A circle has a radius of 5 cm. What is the length of the arc subtended by a central angle of 2 radians?

7. An arc length of 12 cm is subtended by a central angle of (π/3) radians. What is the radius of the circle?

8. A pendulum of length 40 cm swings through an angle of (π/6) radians. What is the length of the arc traced by the pendulum's bob?

9. A circular track has a radius of 100 meters. If a runner completes an arc of 250 meters, what is the angle (in radians) that the runner has covered from the center of the track?

10. An angle of 360 degrees is equivalent to 2π radians.

11. If the radius of a circle is doubled, and the central angle remains the same, the arc length will also double.

12. A car tire has a radius of 30 cm. If the car travels 150 meters, through what angle (in radians) does a point on the tire's circumference rotate? (Hint: Convert meters to centimeters first.)