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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 48 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 48 cm, θ = 270° · L = (θ/360°) × 2πr

  2. 2. A circular sector has radius 36 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 36 cm, θ = 180° · L = (θ/360°) × 2πr

  3. 3. A circular sector has radius 84 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 84 cm, θ = 270° · A = (θ/360°) × πr²

  4. 4. A circular sector has radius 48 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 48 cm, θ = 120° · A = (θ/360°) × πr²

  5. 5. 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

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

    Sector: r = 6 cm, θ = 180° · L = (θ/360°) × 2πr

  7. 7. A circular sector has radius 30 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 30 cm, θ = 180° · L = (θ/360°) × 2πr

  8. 8. A circular sector has radius 12 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 12 cm, θ = 180° · L = (θ/360°) × 2πr

  9. 9. A circular sector has radius 18 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 18 cm, θ = 180° · L = (θ/360°) × 2πr

  10. 10. A circular sector has radius 48 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    Sector: r = 48 cm, θ = 180° · A = (θ/360°) × πr²

  11. 11. A circular sector has radius 78 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 78 cm, θ = 60° · L = (θ/360°) × 2πr

  12. 12. A circular sector has radius 54 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    Sector: r = 54 cm, θ = 90° · L = (θ/360°) × 2πr
12 questions · Seed 42 · 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 48 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    226.08 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 48 = 226.08 cm.

  2. 2. A circular sector has radius 36 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    113.04 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 36 = 113.04 cm.

  3. 3. A circular sector has radius 84 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    16616.88 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 84² = 16616.88 cm².

  4. 4. A circular sector has radius 48 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    2411.52 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 48² = 2411.52 cm².

  5. 5. 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.

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

    18.84 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 6 = 18.84 cm.

  7. 7. A circular sector has radius 30 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    94.2 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 30 = 94.2 cm.

  8. 8. A circular sector has radius 12 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    37.68 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 12 = 37.68 cm.

  9. 9. A circular sector has radius 18 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    56.52 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 18 = 56.52 cm.

  10. 10. A circular sector has radius 48 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    3617.28 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 48² = 3617.28 cm².

  11. 11. A circular sector has radius 78 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    81.64 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 78 = 81.64 cm.

  12. 12. A circular sector has radius 54 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    84.78 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 54 = 84.78 cm.

12 questions · Seed 42 · 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 48 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 48 cm, θ = 270° · L = (θ/360°) × 2πr

  2. 2. A circular sector has radius 36 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 36 cm, θ = 180° · L = (θ/360°) × 2πr

  3. 3. A circular sector has radius 84 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 84 cm, θ = 270° · A = (θ/360°) × πr²

  4. 4. A circular sector has radius 48 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 48 cm, θ = 120° · A = (θ/360°) × πr²

  5. 5. 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

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

    Sector: r = 6 cm, θ = 180° · L = (θ/360°) × 2πr

  7. 7. A circular sector has radius 30 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 30 cm, θ = 180° · L = (θ/360°) × 2πr

  8. 8. A circular sector has radius 12 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 12 cm, θ = 180° · L = (θ/360°) × 2πr

  9. 9. A circular sector has radius 18 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 18 cm, θ = 180° · L = (θ/360°) × 2πr

  10. 10. A circular sector has radius 48 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    Sector: r = 48 cm, θ = 180° · A = (θ/360°) × πr²

  11. 11. A circular sector has radius 78 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 78 cm, θ = 60° · L = (θ/360°) × 2πr

  12. 12. A circular sector has radius 54 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    Sector: r = 54 cm, θ = 90° · L = (θ/360°) × 2πr
12 questions · Seed 42 · 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 48 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    226.08 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 48 = 226.08 cm.

  2. 2. A circular sector has radius 36 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    113.04 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 36 = 113.04 cm.

  3. 3. A circular sector has radius 84 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    16616.88 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 84² = 16616.88 cm².

  4. 4. A circular sector has radius 48 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    2411.52 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 48² = 2411.52 cm².

  5. 5. 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.

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

    18.84 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 6 = 18.84 cm.

  7. 7. A circular sector has radius 30 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    94.2 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 30 = 94.2 cm.

  8. 8. A circular sector has radius 12 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    37.68 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 12 = 37.68 cm.

  9. 9. A circular sector has radius 18 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    56.52 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 18 = 56.52 cm.

  10. 10. A circular sector has radius 48 cm and central angle 180°. Using π = 3.14, calculate its sector area.

    3617.28 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 48² = 3617.28 cm².

  11. 11. A circular sector has radius 78 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    81.64 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 78 = 81.64 cm.

  12. 12. A circular sector has radius 54 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    84.78 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 54 = 84.78 cm.

12 questions · Seed 42 · Age guidance, not curriculum certification