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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 90 cm and central angle 90°. Using π = 3.14, calculate its sector area.

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

  2. 2. A circular sector has radius 18 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 18 cm, θ = 270° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 6 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    Sector: r = 6 cm, θ = 180° · A = (θ/360°) × πr²

  4. 4. A circular sector has radius 48 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 48 cm, θ = 240° · L = (θ/360°) × 2πr

  5. 5. A circular sector has radius 36 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 36 cm, θ = 120° · L = (θ/360°) × 2πr

  6. 6. A circular sector has radius 30 cm and central angle 300°. Using π = 3.14, calculate its arc length.

    Sector: r = 30 cm, θ = 300° · L = (θ/360°) × 2πr

  7. 7. A circular sector has radius 54 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 54 cm, θ = 270° · A = (θ/360°) × πr²

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

    Sector: r = 6 cm, θ = 240° · A = (θ/360°) × πr²

  9. 9. A circular sector has radius 72 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 72 cm, θ = 120° · L = (θ/360°) × 2πr

  10. 10. A circular sector has radius 78 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 78 cm, θ = 180° · L = (θ/360°) × 2πr

  11. 11. A circular sector has radius 24 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    Sector: r = 24 cm, θ = 60° · A = (θ/360°) × πr²

  12. 12. A circular sector has radius 48 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    Sector: r = 48 cm, θ = 90° · L = (θ/360°) × 2πr
12 questions · Seed 46 · 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 90 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    6358.5 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 90² = 6358.5 cm².

  2. 2. A circular sector has radius 18 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    763.02 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 18² = 763.02 cm².

  3. 3. A circular sector has radius 6 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    56.52 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 6² = 56.52 cm².

  4. 4. A circular sector has radius 48 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    200.96 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 48 = 200.96 cm.

  5. 5. A circular sector has radius 36 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    75.36 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 36 = 75.36 cm.

  6. 6. A circular sector has radius 30 cm and central angle 300°. Using π = 3.14, calculate its arc length.

    157 cm

    Arc length L = (300° ÷ 360°) × 2 × 3.14 × 30 = 157 cm.

  7. 7. A circular sector has radius 54 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    6867.18 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 54² = 6867.18 cm².

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

    75.36 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 6² = 75.36 cm².

  9. 9. A circular sector has radius 72 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    150.72 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 72 = 150.72 cm.

  10. 10. A circular sector has radius 78 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    244.92 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 78 = 244.92 cm.

  11. 11. A circular sector has radius 24 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    301.44 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 24² = 301.44 cm².

  12. 12. A circular sector has radius 48 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    75.36 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 48 = 75.36 cm.

12 questions · Seed 46 · 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 90 cm and central angle 90°. Using π = 3.14, calculate its sector area.

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

  2. 2. A circular sector has radius 18 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 18 cm, θ = 270° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 6 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    Sector: r = 6 cm, θ = 180° · A = (θ/360°) × πr²

  4. 4. A circular sector has radius 48 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 48 cm, θ = 240° · L = (θ/360°) × 2πr

  5. 5. A circular sector has radius 36 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 36 cm, θ = 120° · L = (θ/360°) × 2πr

  6. 6. A circular sector has radius 30 cm and central angle 300°. Using π = 3.14, calculate its arc length.

    Sector: r = 30 cm, θ = 300° · L = (θ/360°) × 2πr

  7. 7. A circular sector has radius 54 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 54 cm, θ = 270° · A = (θ/360°) × πr²

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

    Sector: r = 6 cm, θ = 240° · A = (θ/360°) × πr²

  9. 9. A circular sector has radius 72 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    Sector: r = 72 cm, θ = 120° · L = (θ/360°) × 2πr

  10. 10. A circular sector has radius 78 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 78 cm, θ = 180° · L = (θ/360°) × 2πr

  11. 11. A circular sector has radius 24 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    Sector: r = 24 cm, θ = 60° · A = (θ/360°) × πr²

  12. 12. A circular sector has radius 48 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    Sector: r = 48 cm, θ = 90° · L = (θ/360°) × 2πr
12 questions · Seed 46 · 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 90 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    6358.5 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 90² = 6358.5 cm².

  2. 2. A circular sector has radius 18 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    763.02 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 18² = 763.02 cm².

  3. 3. A circular sector has radius 6 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    56.52 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 6² = 56.52 cm².

  4. 4. A circular sector has radius 48 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    200.96 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 48 = 200.96 cm.

  5. 5. A circular sector has radius 36 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    75.36 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 36 = 75.36 cm.

  6. 6. A circular sector has radius 30 cm and central angle 300°. Using π = 3.14, calculate its arc length.

    157 cm

    Arc length L = (300° ÷ 360°) × 2 × 3.14 × 30 = 157 cm.

  7. 7. A circular sector has radius 54 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    6867.18 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 54² = 6867.18 cm².

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

    75.36 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 6² = 75.36 cm².

  9. 9. A circular sector has radius 72 cm and central angle 120°. Using π = 3.14, calculate its arc length.

    150.72 cm

    Arc length L = (120° ÷ 360°) × 2 × 3.14 × 72 = 150.72 cm.

  10. 10. A circular sector has radius 78 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    244.92 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 78 = 244.92 cm.

  11. 11. A circular sector has radius 24 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    301.44 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 24² = 301.44 cm².

  12. 12. A circular sector has radius 48 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    75.36 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 48 = 75.36 cm.

12 questions · Seed 46 · Age guidance, not curriculum certification