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MathsAges 13-15

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.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 13-15

Circle arc length & sector area

Take your time. Show your thinking.

  1. 1. A circular sector has radius 12 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 12 cm, θ = 60° · L = (θ/360°) × 2πr

  2. 2. A circular sector has radius 66 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 66 cm, θ = 90° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 66 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 66 cm, θ = 240° · L = (θ/360°) × 2πr

  4. 4. 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

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

    Sector: r = 90 cm, θ = 120° · L = (θ/360°) × 2πr

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

    Sector: r = 84 cm, θ = 60° · A = (θ/360°) × πr²

  7. 7. A circular sector has radius 72 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    Sector: r = 72 cm, θ = 180° · A = (θ/360°) × πr²

  8. 8. A circular sector has radius 42 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 42 cm, θ = 180° · L = (θ/360°) × 2πr

  9. 9. A circular sector has radius 60 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    Sector: r = 60 cm, θ = 180° · A = (θ/360°) × πr²

  10. 10. A circular sector has radius 78 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 78 cm, θ = 270° · L = (θ/360°) × 2πr

  11. 11. A circular sector has radius 84 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 84 cm, θ = 180° · L = (θ/360°) × 2πr

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

    Sector: r = 84 cm, θ = 120° · A = (θ/360°) × πr²
12 questions · Seed 104730 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Circle arc length & sector area

Answers and reasoning. Review before teaching.

  1. 1. A circular sector has radius 12 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    12.56 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 12 = 12.56 cm.

  2. 2. A circular sector has radius 66 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    3419.46 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 66² = 3419.46 cm².

  3. 3. A circular sector has radius 66 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    276.32 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 66 = 276.32 cm.

  4. 4. 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.

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

    188.4 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 90 = 188.4 cm.

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

    3692.64 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 84² = 3692.64 cm².

  7. 7. A circular sector has radius 72 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    8138.88 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 72² = 8138.88 cm².

  8. 8. A circular sector has radius 42 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    131.88 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 42 = 131.88 cm.

  9. 9. A circular sector has radius 60 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    5652 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 60² = 5652 cm².

  10. 10. A circular sector has radius 78 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    367.38 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 78 = 367.38 cm.

  11. 11. A circular sector has radius 84 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    263.76 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 84 = 263.76 cm.

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

    7385.28 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 84² = 7385.28 cm².

12 questions · Seed 104730 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Circle arc length & sector area

Take your time. Show your thinking.

  1. 1. A circular sector has radius 12 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 12 cm, θ = 60° · L = (θ/360°) × 2πr

  2. 2. A circular sector has radius 66 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 66 cm, θ = 90° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 66 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 66 cm, θ = 240° · L = (θ/360°) × 2πr

  4. 4. 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

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

    Sector: r = 90 cm, θ = 120° · L = (θ/360°) × 2πr

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

    Sector: r = 84 cm, θ = 60° · A = (θ/360°) × πr²

  7. 7. A circular sector has radius 72 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    Sector: r = 72 cm, θ = 180° · A = (θ/360°) × πr²

  8. 8. A circular sector has radius 42 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 42 cm, θ = 180° · L = (θ/360°) × 2πr

  9. 9. A circular sector has radius 60 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    Sector: r = 60 cm, θ = 180° · A = (θ/360°) × πr²

  10. 10. A circular sector has radius 78 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 78 cm, θ = 270° · L = (θ/360°) × 2πr

  11. 11. A circular sector has radius 84 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 84 cm, θ = 180° · L = (θ/360°) × 2πr

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

    Sector: r = 84 cm, θ = 120° · A = (θ/360°) × πr²
12 questions · Seed 104730 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Circle arc length & sector area

Answers and reasoning. Review before teaching.

  1. 1. A circular sector has radius 12 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    12.56 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 12 = 12.56 cm.

  2. 2. A circular sector has radius 66 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    3419.46 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 66² = 3419.46 cm².

  3. 3. A circular sector has radius 66 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    276.32 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 66 = 276.32 cm.

  4. 4. 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.

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

    188.4 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 90 = 188.4 cm.

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

    3692.64 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 84² = 3692.64 cm².

  7. 7. A circular sector has radius 72 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    8138.88 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 72² = 8138.88 cm².

  8. 8. A circular sector has radius 42 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    131.88 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 42 = 131.88 cm.

  9. 9. A circular sector has radius 60 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    5652 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 60² = 5652 cm².

  10. 10. A circular sector has radius 78 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    367.38 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 78 = 367.38 cm.

  11. 11. A circular sector has radius 84 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    263.76 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 84 = 263.76 cm.

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

    7385.28 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 84² = 7385.28 cm².

12 questions · Seed 104730 · Age guidance, not curriculum certification