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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 84 cm and central angle 60°. Using π = 3.14, calculate its arc length.

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

  2. 2. 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

  3. 3. A circular sector has radius 66 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    Sector: r = 66 cm, θ = 60° · A = (θ/360°) × πr²

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

    Sector: r = 66 cm, θ = 90° · L = (θ/360°) × 2πr

  5. 5. A circular sector has radius 24 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 24 cm, θ = 120° · A = (θ/360°) × πr²

  6. 6. A circular sector has radius 66 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    Sector: r = 66 cm, θ = 300° · A = (θ/360°) × πr²

  7. 7. A circular sector has radius 24 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    Sector: r = 24 cm, θ = 240° · A = (θ/360°) × πr²

  8. 8. 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

  9. 9. A circular sector has radius 48 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    Sector: r = 48 cm, θ = 300° · A = (θ/360°) × πr²

  10. 10. A circular sector has radius 12 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 12 cm, θ = 270° · L = (θ/360°) × 2πr

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

    Sector: r = 6 cm, θ = 90° · A = (θ/360°) × πr²

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

    Sector: r = 48 cm, θ = 240° · A = (θ/360°) × πr²
12 questions · Seed 45 · 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 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.

  2. 2. 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.

  3. 3. A circular sector has radius 66 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    2279.64 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 66² = 2279.64 cm².

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

    103.62 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 66 = 103.62 cm.

  5. 5. A circular sector has radius 24 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    602.88 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 24² = 602.88 cm².

  6. 6. A circular sector has radius 66 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    11398.2 cm²

    Sector area A = (300° ÷ 360°) × 3.14 × 66² = 11398.2 cm².

  7. 7. A circular sector has radius 24 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    1205.76 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 24² = 1205.76 cm².

  8. 8. 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.

  9. 9. A circular sector has radius 48 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    6028.8 cm²

    Sector area A = (300° ÷ 360°) × 3.14 × 48² = 6028.8 cm².

  10. 10. A circular sector has radius 12 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    56.52 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 12 = 56.52 cm.

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

    28.26 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 6² = 28.26 cm².

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

    4823.04 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 48² = 4823.04 cm².

12 questions · Seed 45 · 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 84 cm and central angle 60°. Using π = 3.14, calculate its arc length.

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

  2. 2. 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

  3. 3. A circular sector has radius 66 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    Sector: r = 66 cm, θ = 60° · A = (θ/360°) × πr²

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

    Sector: r = 66 cm, θ = 90° · L = (θ/360°) × 2πr

  5. 5. A circular sector has radius 24 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 24 cm, θ = 120° · A = (θ/360°) × πr²

  6. 6. A circular sector has radius 66 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    Sector: r = 66 cm, θ = 300° · A = (θ/360°) × πr²

  7. 7. A circular sector has radius 24 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    Sector: r = 24 cm, θ = 240° · A = (θ/360°) × πr²

  8. 8. 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

  9. 9. A circular sector has radius 48 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    Sector: r = 48 cm, θ = 300° · A = (θ/360°) × πr²

  10. 10. A circular sector has radius 12 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 12 cm, θ = 270° · L = (θ/360°) × 2πr

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

    Sector: r = 6 cm, θ = 90° · A = (θ/360°) × πr²

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

    Sector: r = 48 cm, θ = 240° · A = (θ/360°) × πr²
12 questions · Seed 45 · 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 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.

  2. 2. 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.

  3. 3. A circular sector has radius 66 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    2279.64 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 66² = 2279.64 cm².

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

    103.62 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 66 = 103.62 cm.

  5. 5. A circular sector has radius 24 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    602.88 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 24² = 602.88 cm².

  6. 6. A circular sector has radius 66 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    11398.2 cm²

    Sector area A = (300° ÷ 360°) × 3.14 × 66² = 11398.2 cm².

  7. 7. A circular sector has radius 24 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    1205.76 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 24² = 1205.76 cm².

  8. 8. 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.

  9. 9. A circular sector has radius 48 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    6028.8 cm²

    Sector area A = (300° ÷ 360°) × 3.14 × 48² = 6028.8 cm².

  10. 10. A circular sector has radius 12 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    56.52 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 12 = 56.52 cm.

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

    28.26 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 6² = 28.26 cm².

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

    4823.04 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 48² = 4823.04 cm².

12 questions · Seed 45 · Age guidance, not curriculum certification