Grade 10 · Math · Geometry

10th grade Radians and degrees worksheet

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Radians and degrees

Grade 10 Math Worksheet

NameDate

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

Milo watches a clock hand move from 12 to 7: a turn of 210°. How many radians is 210°, in terms of π?
Noah turns a bike pedal part of the way round: a turn of 225°. How many radians is 225°, in terms of π?
Pia spins a spinner most of the way round: a turn of 300°. How many radians is 300°, in terms of π?
Ren draws a star, turning 72° at its center between points: a turn of 72°. How many radians is 72°, in terms of π?
Tala opens a gate through an angle of 5π/6 radians. How many degrees is that?
Ari turns a clock hand through an angle of 2π/9 radians. How many degrees is that?
Bo spins a spinner through an angle of 11π/12 radians. How many degrees is that?
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?
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?
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?

Radians and degrees. Every version has 10 questions, and the answer key prints on the second page.

Standard: G-C.B.5, F-TF.A.1

radian: The angle that holds an arc one radius long.

π radians: A half turn, 180°.

2π radians: A whole turn, 360°.

s = rθ: Arc length = radius × angle, with the angle in radians.

in terms of π: Keep π as a letter in the answer, like 5π/6.

Your child wrote π next to the degree number instead of converting.

Your child treated π radians as a full turn.

Your child divided by 180 but left π off the answer.

Ask: how many degrees make π radians?

Ask: π radians is half a turn; how many degrees is that?

Ask: 180° is how many radians?

What is the most common mistake with radians and degrees?

Your child wrote π next to the degree number instead of converting.

How can I help my child with radians and degrees?

Ask: how many degrees make π radians?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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