Grade 10 · Math · Geometry

10th grade Radians and degrees worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

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Radians and degrees

Grade 10 Math Worksheet - Challenge Me

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

Milo pipes icing on a cookie's edge. The circle has radius 5 cm; ∠COD = 72°. Using s = rθ, how long is arc CD in cm, in terms of π?
Noah sews trim on a round rug. The circle has radius 8 cm; ∠COD = 150°. Using s = rθ, how long is arc CD in cm, in terms of π?
Pia paints a long curve on a small plate. The circle has radius 3 cm; ∠COD = 240°. Using s = rθ, how long is arc CD in cm, in terms of π?
Ren walks part way round a round pond. The circle has radius 14 m; ∠COD = 90°. Using s = rθ, how long is arc CD in meters, in terms of π?
Tala rolls a bike wheel. An arc 12 cm long has a central angle of 3/2 radians. What is the radius, in cm?
Ari measures a curve on a clock face. An arc 14 cm long has a central angle of 7/4 radians. What is the radius, in cm?
Bo measures icing on a cookie's edge. An arc 9 cm long has a central angle of 3/4 radians. What is the radius, in cm?
Esme measures trim on a round rug. Arc CD is 5π in. long on a circle of radius 9 in. How many degrees is ∠COD?
Jun walks a curved path. Arc CD is 4π m long on a circle of radius 15 m. How many degrees is ∠COD?
Kira cuts a wedge of a round cake. Arc CD is 3π in. long on a circle of radius 4 in. How many degrees is ∠COD?

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.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records