Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
MathsAges 16-18

Circle arc length & sector area

Use θ ÷ 360° with π = 3.14 to calculate the arc length or area of a circular sector. Review suitability for your learners before teaching.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Circle arc length & sector area

Take your time. Show your thinking.

  1. 1. A circular sector has radius 24 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 24 cm, θ = 270° · L = (θ/360°) × 2πr

  2. 2. A circular sector has radius 84 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 84 cm, θ = 120° · L = (θ/360°) × 2πr

  3. 3. A circular sector has radius 30 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 30 cm, θ = 90° · A = (θ/360°) × πr²

  4. 4. A circular sector has radius 84 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 84 cm, θ = 60° · L = (θ/360°) × 2πr

  5. 5. A circular sector has radius 6 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 6 cm, θ = 120° · L = (θ/360°) × 2πr

  6. 6. A circular sector has radius 90 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 90 cm, θ = 240° · L = (θ/360°) × 2πr

  7. 7. A circular sector has radius 30 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 30 cm, θ = 60° · L = (θ/360°) × 2πr

  8. 8. A circular sector has radius 84 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 84 cm, θ = 240° · L = (θ/360°) × 2πr

  9. 9. A circular sector has radius 54 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 54 cm, θ = 120° · L = (θ/360°) × 2πr

  10. 10. A circular sector has radius 18 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 18 cm, θ = 120° · A = (θ/360°) × πr²

  11. 11. A circular sector has radius 6 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 6 cm, θ = 270° · L = (θ/360°) × 2πr

  12. 12. A circular sector has radius 90 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 90 cm, θ = 120° · A = (θ/360°) × πr²
12 questions · Seed 44 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Circle arc length & sector area

Answers and reasoning. Review before teaching.

  1. 1. A circular sector has radius 24 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    113.04 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 24 = 113.04 cm.

  2. 2. A circular sector has radius 84 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    175.84 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 84 = 175.84 cm.

  3. 3. A circular sector has radius 30 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    706.5 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 30² = 706.5 cm².

  4. 4. A circular sector has radius 84 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    87.92 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 84 = 87.92 cm.

  5. 5. A circular sector has radius 6 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    12.56 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 6 = 12.56 cm.

  6. 6. A circular sector has radius 90 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    376.8 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 90 = 376.8 cm.

  7. 7. A circular sector has radius 30 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    31.4 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 30 = 31.4 cm.

  8. 8. A circular sector has radius 84 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    351.68 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 84 = 351.68 cm.

  9. 9. A circular sector has radius 54 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    113.04 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 54 = 113.04 cm.

  10. 10. A circular sector has radius 18 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    339.12 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 18² = 339.12 cm².

  11. 11. A circular sector has radius 6 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    28.26 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 6 = 28.26 cm.

  12. 12. A circular sector has radius 90 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    8478 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 90² = 8478 cm².

12 questions · Seed 44 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Circle arc length & sector area

Take your time. Show your thinking.

  1. 1. A circular sector has radius 24 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 24 cm, θ = 270° · L = (θ/360°) × 2πr

  2. 2. A circular sector has radius 84 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 84 cm, θ = 120° · L = (θ/360°) × 2πr

  3. 3. A circular sector has radius 30 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 30 cm, θ = 90° · A = (θ/360°) × πr²

  4. 4. A circular sector has radius 84 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 84 cm, θ = 60° · L = (θ/360°) × 2πr

  5. 5. A circular sector has radius 6 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 6 cm, θ = 120° · L = (θ/360°) × 2πr

  6. 6. A circular sector has radius 90 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 90 cm, θ = 240° · L = (θ/360°) × 2πr

  7. 7. A circular sector has radius 30 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 30 cm, θ = 60° · L = (θ/360°) × 2πr

  8. 8. A circular sector has radius 84 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 84 cm, θ = 240° · L = (θ/360°) × 2πr

  9. 9. A circular sector has radius 54 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 54 cm, θ = 120° · L = (θ/360°) × 2πr

  10. 10. A circular sector has radius 18 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 18 cm, θ = 120° · A = (θ/360°) × πr²

  11. 11. A circular sector has radius 6 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 6 cm, θ = 270° · L = (θ/360°) × 2πr

  12. 12. A circular sector has radius 90 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 90 cm, θ = 120° · A = (θ/360°) × πr²
12 questions · Seed 44 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Circle arc length & sector area

Answers and reasoning. Review before teaching.

  1. 1. A circular sector has radius 24 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    113.04 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 24 = 113.04 cm.

  2. 2. A circular sector has radius 84 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    175.84 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 84 = 175.84 cm.

  3. 3. A circular sector has radius 30 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    706.5 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 30² = 706.5 cm².

  4. 4. A circular sector has radius 84 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    87.92 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 84 = 87.92 cm.

  5. 5. A circular sector has radius 6 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    12.56 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 6 = 12.56 cm.

  6. 6. A circular sector has radius 90 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    376.8 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 90 = 376.8 cm.

  7. 7. A circular sector has radius 30 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    31.4 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 30 = 31.4 cm.

  8. 8. A circular sector has radius 84 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    351.68 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 84 = 351.68 cm.

  9. 9. A circular sector has radius 54 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    113.04 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 54 = 113.04 cm.

  10. 10. A circular sector has radius 18 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    339.12 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 18² = 339.12 cm².

  11. 11. A circular sector has radius 6 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    28.26 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 6 = 28.26 cm.

  12. 12. A circular sector has radius 90 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    8478 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 90² = 8478 cm².

12 questions · Seed 44 · Age guidance, not curriculum certification