Radians and degrees

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Milo turns a clock hand from 12 to 1: a turn of 30°. How many radians is 30°, in terms of π?

   π/6
2. 2.

   Noah swings a door open wide: a turn of 135°. How many radians is 135°, in terms of π?

   3π/4
3. 3.

   Pia turns a bike wheel three quarters of the way round: a turn of 270°. How many radians is 270°, in terms of π?

   3π/2
4. 4.

   Ren gives a spinner a small nudge: a turn of 40°. How many radians is 40°, in terms of π?

   2π/9
5. 5.

   Tala rolls a bike wheel of radius 4 inches. A point on the rim moves 9 inches along the circle. How many radians does the wheel turn?

   9/4
6. 6.

   Zee runs a finger along a drum's rim. Arc CD is 18 cm long, and the radius is 6 cm. How many radians is ∠COD?

   3
7. 7.

   Bo lays string along a round clock's edge. Arc CD is 15 cm long, and the radius is 10 cm. How many radians is ∠COD?

   3/2
8. 8.

   Esme cuts a round pizza into 4 equal slices. That is 1/4 of the whole turn. How many radians is that angle at the center, in terms of π?

   π/2
9. 9.

   Kira eats 3 of 8 equal pizza slices. That is 3/8 of the whole turn. How many radians is that angle at the center, in terms of π?

   3π/4
10. 10.

    Luz watches a clock hand move from 12 to 5. That is 5/12 of the whole turn. How many radians is that angle at the center, in terms of π?

    5π/6