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Grade 10 Arc Length & Sector Area Worksheet with Answers

Grade 10 (US) · Year 11 (UK) · Class 10 (India) · Math

Unit 5: Polygons & CirclesCirclesCCSS G-C.B.5

Finding arc lengths and sector areas as fractions of a circle, in terms of π. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Arc Length & Sector Area

Grade 10 · Math

Score___ / 12

Name

Class

Date

Learning goal: Circles · CCSS G-C.B.5

Directions: Use the pictures to help you. Solve each problem. Show your work, then write your answer in the box.

Example

Find the length of an arc with central angle 45° in a circle of radius 4. Leave your answer in terms of π.

Answer: π

RememberCircles

rdRadius r: centre to edgeDiameter d = 2rCircumference C = 2πr = πdArea A = πr²Sector = (angle ÷ 360) × πr²
  1. 1

    Find the length of an arc with central angle 120° in a circle of radius 3. Leave your answer in terms of π.

    120°r = 3
    Answer
  2. 2

    Find the length of an arc with central angle 45° in a circle of radius 5. Leave your answer in terms of π.

    45°r = 5
    Answer
  3. 3

    A circle has radius 11. What fraction of the circumference is an arc with central angle 120°?

    Show your work
    Answer
  4. 4

    Find the length of an arc with central angle 150° in a circle of radius 6. Leave your answer in terms of π.

    150°r = 6
    Answer
  5. 5

    Find the length of an arc with central angle 240° in a circle of radius 11. Leave your answer in terms of π.

    240°r = 11
    Answer
  6. 6

    A circle has radius 10. What fraction of the circumference is an arc with central angle 120°?

    Show your work
    Answer
  7. 7

    Find the area of a sector with central angle 90° in a circle of radius 12. Leave your answer in terms of π.

    90°r = 12
    Answer
  8. 8

    Find the length of an arc with central angle 120° in a circle of radius 12. Leave your answer in terms of π.

    120°r = 12
    Answer
  9. 9

    A circle has radius 7. What fraction of the circumference is an arc with central angle 240°?

    Show your work
    Answer
  10. 10

    Find the length of an arc with central angle 240° in a circle of radius 7. Leave your answer in terms of π.

    240°r = 7
    Answer
  11. 11

    Find the length of an arc with central angle 120° in a circle of radius 4. Leave your answer in terms of π.

    120°r = 4
    Answer
  12. 12

    A circle has radius 8. What fraction of the circumference is an arc with central angle 180°?

    Show your work
    Answer

★ Challenge corner for fast finishers

How many different ways can the letters of the word CODE be arranged? (all letters are different)

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/10/arc_sector

Answer key (click to show)
  1. 1.2π
  2. 2.5π/4
  3. 3.1/3
  4. 4.5π
  5. 5.44π/3
  6. 6.1/3
  7. 7.36π
  8. 8.8π
  9. 9.2/3
  10. 10.28π/3
  11. 11.8π/3
  12. 12.1/2
  13. ★24 (challenge corner)

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