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Year 10 · Measurement

Arc length and sector area

A sector is a slice of a circle. Its arc and area are fractions of the whole circle.

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How to do it

  1. Fraction = angle ÷ 360.
  2. Arc length = fraction × 2πr. Area = fraction × πr².

Worked example

A sector has radius 10 cm and angle 45°. Find the arc length in cm (π ≈ 3.14, one decimal place).
Arc = θ/360 × 2πr = 45/360 × 2 × 3.14 × 10 ≈ 7.9.
Answer: 7.9

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Use the angle over 360, not over 180.

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