Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
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.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Circle arc length & sector area

Take your time. Show your thinking.

  1. 1. 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

  2. 2. A circular sector has radius 78 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    Sector: r = 78 cm, θ = 240° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 60 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 60 cm, θ = 120° · A = (θ/360°) × πr²

  4. 4. 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

  5. 5. A circular sector has radius 60 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    Sector: r = 60 cm, θ = 240° · A = (θ/360°) × πr²

  6. 6. A circular sector has radius 66 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 66 cm, θ = 270° · L = (θ/360°) × 2πr

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

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

  8. 8. 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

  9. 9. A circular sector has radius 54 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    Sector: r = 54 cm, θ = 60° · A = (θ/360°) × πr²

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

    Sector: r = 6 cm, θ = 240° · L = (θ/360°) × 2πr

  11. 11. A circular sector has radius 42 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    Sector: r = 42 cm, θ = 300° · A = (θ/360°) × πr²

  12. 12. A circular sector has radius 78 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 78 cm, θ = 90° · A = (θ/360°) × πr²
12 questions · Seed 49 · 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 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.

  2. 2. A circular sector has radius 78 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    12735.84 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 78² = 12735.84 cm².

  3. 3. A circular sector has radius 60 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    3768 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 60² = 3768 cm².

  4. 4. 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.

  5. 5. A circular sector has radius 60 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    7536 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 60² = 7536 cm².

  6. 6. A circular sector has radius 66 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    310.86 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 66 = 310.86 cm.

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

    4239 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 90² = 4239 cm².

  8. 8. 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.

  9. 9. A circular sector has radius 54 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    1526.04 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 54² = 1526.04 cm².

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

    25.12 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 6 = 25.12 cm.

  11. 11. A circular sector has radius 42 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    4615.8 cm²

    Sector area A = (300° ÷ 360°) × 3.14 × 42² = 4615.8 cm².

  12. 12. A circular sector has radius 78 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    4775.94 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 78² = 4775.94 cm².

12 questions · Seed 49 · 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 54 cm and central angle 270°. Using π = 3.14, calculate its sector area.

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

  2. 2. A circular sector has radius 78 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    Sector: r = 78 cm, θ = 240° · A = (θ/360°) × πr²

  3. 3. A circular sector has radius 60 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    Sector: r = 60 cm, θ = 120° · A = (θ/360°) × πr²

  4. 4. 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

  5. 5. A circular sector has radius 60 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    Sector: r = 60 cm, θ = 240° · A = (θ/360°) × πr²

  6. 6. A circular sector has radius 66 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    Sector: r = 66 cm, θ = 270° · L = (θ/360°) × 2πr

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

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

  8. 8. 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

  9. 9. A circular sector has radius 54 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    Sector: r = 54 cm, θ = 60° · A = (θ/360°) × πr²

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

    Sector: r = 6 cm, θ = 240° · L = (θ/360°) × 2πr

  11. 11. A circular sector has radius 42 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    Sector: r = 42 cm, θ = 300° · A = (θ/360°) × πr²

  12. 12. A circular sector has radius 78 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    Sector: r = 78 cm, θ = 90° · A = (θ/360°) × πr²
12 questions · Seed 49 · 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 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.

  2. 2. A circular sector has radius 78 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    12735.84 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 78² = 12735.84 cm².

  3. 3. A circular sector has radius 60 cm and central angle 120°. Using π = 3.14, calculate its sector area.

    3768 cm²

    Sector area A = (120° ÷ 360°) × 3.14 × 60² = 3768 cm².

  4. 4. 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.

  5. 5. A circular sector has radius 60 cm and central angle 240°. Using π = 3.14, calculate its sector area.

    7536 cm²

    Sector area A = (240° ÷ 360°) × 3.14 × 60² = 7536 cm².

  6. 6. A circular sector has radius 66 cm and central angle 270°. Using π = 3.14, calculate its arc length.

    310.86 cm

    Arc length L = (270° ÷ 360°) × 2 × 3.14 × 66 = 310.86 cm.

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

    4239 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 90² = 4239 cm².

  8. 8. 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.

  9. 9. A circular sector has radius 54 cm and central angle 60°. Using π = 3.14, calculate its sector area.

    1526.04 cm²

    Sector area A = (60° ÷ 360°) × 3.14 × 54² = 1526.04 cm².

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

    25.12 cm

    Arc length L = (240° ÷ 360°) × 2 × 3.14 × 6 = 25.12 cm.

  11. 11. A circular sector has radius 42 cm and central angle 300°. Using π = 3.14, calculate its sector area.

    4615.8 cm²

    Sector area A = (300° ÷ 360°) × 3.14 × 42² = 4615.8 cm².

  12. 12. A circular sector has radius 78 cm and central angle 90°. Using π = 3.14, calculate its sector area.

    4775.94 cm²

    Sector area A = (90° ÷ 360°) × 3.14 × 78² = 4775.94 cm².

12 questions · Seed 49 · Age guidance, not curriculum certification