Radians and degrees

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Noah turns a bike pedal part of the way round: a turn of 225°. How many radians is 225°, in terms of π?

   5π/4
2. 2.

   Ren draws a star, turning 72° at its center between points: a turn of 72°. How many radians is 72°, in terms of π?

   2π/5
3. 3.

   Tala opens a gate through an angle of 5π/6 radians. How many degrees is that?

   150
4. 4.

   Zee turns a bike wheel through an angle of 7π/4 radians. How many degrees is that?

   315
5. 5.

   Ari turns a clock hand through an angle of 2π/9 radians. How many degrees is that?

   40
6. 6.

   Bo spins a spinner through an angle of 11π/12 radians. How many degrees is that?

   165
7. 7.

   Esme cuts a pizza slice. Circle O has radius 6 cm, and ∠COD = 2π/3 radians. How long is arc CD in cm, in terms of π?

   4π
8. 8.

   Jun sews trim on part of a round rug. Circle O has radius 10 cm, and ∠COD = 3π/4 radians. How long is arc CD in cm, in terms of π?

   15π/2
9. 9.

   Kira glues ribbon on part of a drum's rim. Circle O has radius 8 cm, and ∠COD = 5π/6 radians. How long is arc CD in cm, in terms of π?

   20π/3
10. 10.

    Luz paints part of a clock's rim. Circle O has radius 12 cm, and ∠COD = 3π/8 radians. How long is arc CD in cm, in terms of π?

    9π/2