Arcs and sectors

A sector is a slice of a circle, like a slice of pizza, and an arc is the curved part of its edge. Both are a fraction of the whole circle: the angle out of 360°.

Key facts

  • Arc length = θ/360 × 2πr.
  • Sector area = θ/360 × πr².
  • Perimeter of a sector = arc + two radii.

Worked examples

Example 1

A sector has radius 6 cm and angle 120°. Find its area and arc length, in terms of π.

  1. 120° is a third of 360°.
  2. Area: a third of π × 6² = 36π. 12π cm²
  3. Arc: a third of 2π × 6 = 12π. 4π cm

Answer: 12π cm² and 4π cm