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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 18 cm and central angle 180°. Using π = 3.14, calculate its arc length.

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

  2. 2. A circular sector has radius 42 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 42 cm, θ = 270° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 42 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 42 cm, θ = 270° · L = (θ/360°) × 2πr

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

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

  5. 5. A circular sector has radius 54 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 54 cm, θ = 180° · L = (θ/360°) × 2πr

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

    Sector: r = 12 cm, θ = 60° · A = (θ/360°) × πr²

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

    Sector: r = 36 cm, θ = 180° · A = (θ/360°) × πr²

  8. 8. A circular sector has radius 90 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 90 cm, θ = 60° · L = (θ/360°) × 2πr

  9. 9. A circular sector has radius 72 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 72 cm, θ = 270° · A = (θ/360°) × πr²

  10. 10. A circular sector has radius 36 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 36 cm, θ = 90° · A = (θ/360°) × πr²

  11. 11. A circular sector has radius 54 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 54 cm, θ = 240° · L = (θ/360°) × 2πr

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

    Sector: r = 24 cm, θ = 270° · A = (θ/360°) × πr²
12 questions · Seed 52 · 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 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.

  2. 2. A circular sector has radius 42 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    4154.22 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 42² = 4154.22 cm².

  3. 3. A circular sector has radius 42 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    197.82 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 42 = 197.82 cm.

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

    1884 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 60² = 1884 cm².

  5. 5. A circular sector has radius 54 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    169.56 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 54 = 169.56 cm.

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

    75.36 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 12² = 75.36 cm².

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

    2034.72 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 36² = 2034.72 cm².

  8. 8. A circular sector has radius 90 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    94.2 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 90 = 94.2 cm.

  9. 9. A circular sector has radius 72 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    12208.32 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 72² = 12208.32 cm².

  10. 10. A circular sector has radius 36 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    1017.36 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 36² = 1017.36 cm².

  11. 11. A circular sector has radius 54 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    226.08 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 54 = 226.08 cm.

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

    1356.48 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 24² = 1356.48 cm².

12 questions · Seed 52 · 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 18 cm and central angle 180°. Using π = 3.14, calculate its arc length.

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

  2. 2. A circular sector has radius 42 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 42 cm, θ = 270° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 42 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 42 cm, θ = 270° · L = (θ/360°) × 2πr

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

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

  5. 5. A circular sector has radius 54 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    Sector: r = 54 cm, θ = 180° · L = (θ/360°) × 2πr

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

    Sector: r = 12 cm, θ = 60° · A = (θ/360°) × πr²

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

    Sector: r = 36 cm, θ = 180° · A = (θ/360°) × πr²

  8. 8. A circular sector has radius 90 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    Sector: r = 90 cm, θ = 60° · L = (θ/360°) × 2πr

  9. 9. A circular sector has radius 72 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    Sector: r = 72 cm, θ = 270° · A = (θ/360°) × πr²

  10. 10. A circular sector has radius 36 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 36 cm, θ = 90° · A = (θ/360°) × πr²

  11. 11. A circular sector has radius 54 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    Sector: r = 54 cm, θ = 240° · L = (θ/360°) × 2πr

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

    Sector: r = 24 cm, θ = 270° · A = (θ/360°) × πr²
12 questions · Seed 52 · 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 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.

  2. 2. A circular sector has radius 42 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    4154.22 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 42² = 4154.22 cm².

  3. 3. A circular sector has radius 42 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    197.82 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 42 = 197.82 cm.

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

    1884 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 60² = 1884 cm².

  5. 5. A circular sector has radius 54 cm and central angle 180°. Using π = 3.14, calculate its arc length.

    169.56 cm

    Arc length L = (180° ÷ 360°) × 2 × 3.14 × 54 = 169.56 cm.

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

    75.36 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 12² = 75.36 cm².

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

    2034.72 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 36² = 2034.72 cm².

  8. 8. A circular sector has radius 90 cm and central angle 60°. Using π = 3.14, calculate its arc length.

    94.2 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 90 = 94.2 cm.

  9. 9. A circular sector has radius 72 cm and central angle 270°. Using π = 3.14, calculate its sector area.

    12208.32 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 72² = 12208.32 cm².

  10. 10. A circular sector has radius 36 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    1017.36 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 36² = 1017.36 cm².

  11. 11. A circular sector has radius 54 cm and central angle 240°. Using π = 3.14, calculate its arc length.

    226.08 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 54 = 226.08 cm.

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

    1356.48 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 24² = 1356.48 cm².

12 questions · Seed 52 · Age guidance, not curriculum certification