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MathsAges 16-18

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 16-18

Circle arc length & sector area

Take your time. Show your thinking.

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

    Sector: r = 12 cm, θ = 270° · A = (θ/360°) × πr²

  2. 2. A circular sector has radius 18 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 18 cm, θ = 90° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 24 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    Sector: r = 24 cm, θ = 90° · L = (θ/360°) × 2πr

  4. 4. A circular sector has radius 30 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 30 cm, θ = 90° · A = (θ/360°) × πr²

  5. 5. 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

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

    Sector: r = 30 cm, θ = 180° · A = (θ/360°) × πr²

  7. 7. A circular sector has radius 18 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    Sector: r = 18 cm, θ = 90° · L = (θ/360°) × 2πr

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

    Sector: r = 60 cm, θ = 90° · A = (θ/360°) × πr²

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

    Sector: r = 66 cm, θ = 60° · L = (θ/360°) × 2πr

  10. 10. 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

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

    Sector: r = 24 cm, θ = 240° · L = (θ/360°) × 2πr

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

    Sector: r = 78 cm, θ = 270° · A = (θ/360°) × πr²
12 questions · Seed 50 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Circle arc length & sector area

Answers and reasoning. Review before teaching.

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

    339.12 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 12² = 339.12 cm².

  2. 2. A circular sector has radius 18 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    254.34 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 18² = 254.34 cm².

  3. 3. A circular sector has radius 24 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    37.68 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 24 = 37.68 cm.

  4. 4. A circular sector has radius 30 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    706.5 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 30² = 706.5 cm².

  5. 5. 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.

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

    1413 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 30² = 1413 cm².

  7. 7. A circular sector has radius 18 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    28.26 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 18 = 28.26 cm.

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

    2826 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 60² = 2826 cm².

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

    69.08 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 66 = 69.08 cm.

  10. 10. 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.

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

    100.48 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 24 = 100.48 cm.

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

    14327.82 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 78² = 14327.82 cm².

12 questions · Seed 50 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Circle arc length & sector area

Take your time. Show your thinking.

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

    Sector: r = 12 cm, θ = 270° · A = (θ/360°) × πr²

  2. 2. A circular sector has radius 18 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 18 cm, θ = 90° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 24 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    Sector: r = 24 cm, θ = 90° · L = (θ/360°) × 2πr

  4. 4. A circular sector has radius 30 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 30 cm, θ = 90° · A = (θ/360°) × πr²

  5. 5. 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

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

    Sector: r = 30 cm, θ = 180° · A = (θ/360°) × πr²

  7. 7. A circular sector has radius 18 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    Sector: r = 18 cm, θ = 90° · L = (θ/360°) × 2πr

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

    Sector: r = 60 cm, θ = 90° · A = (θ/360°) × πr²

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

    Sector: r = 66 cm, θ = 60° · L = (θ/360°) × 2πr

  10. 10. 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

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

    Sector: r = 24 cm, θ = 240° · L = (θ/360°) × 2πr

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

    Sector: r = 78 cm, θ = 270° · A = (θ/360°) × πr²
12 questions · Seed 50 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Circle arc length & sector area

Answers and reasoning. Review before teaching.

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

    339.12 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 12² = 339.12 cm².

  2. 2. A circular sector has radius 18 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    254.34 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 18² = 254.34 cm².

  3. 3. A circular sector has radius 24 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    37.68 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 24 = 37.68 cm.

  4. 4. A circular sector has radius 30 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    706.5 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 30² = 706.5 cm².

  5. 5. 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.

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

    1413 cm²

    Sector area A = (180° ÷ 360°) × 3.14 × 30² = 1413 cm².

  7. 7. A circular sector has radius 18 cm and central angle 90°. Using π = 3.14, calculate its arc length.

    28.26 cm

    Arc length L = (90° ÷ 360°) × 2 × 3.14 × 18 = 28.26 cm.

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

    2826 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 60² = 2826 cm².

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

    69.08 cm

    Arc length L = (60° ÷ 360°) × 2 × 3.14 × 66 = 69.08 cm.

  10. 10. 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.

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

    100.48 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 24 = 100.48 cm.

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

    14327.82 cm²

    Sector area A = (270° ÷ 360°) × 3.14 × 78² = 14327.82 cm².

12 questions · Seed 50 · Age guidance, not curriculum certification