Sectors: a fraction of a circle
A standard method from Arcs, sectors and mensuration: the steps and worked examples.
Steps
Fraction = θ / 360°.
- Arc length = 2πr × θ/360°
- Sector area = πr² × θ/360°
- Sector perimeter = arc + 2r
Worked examples
Example 1: A sector has radius 9 cm and angle 80°.
arc = 2π(9) × 80/360 = 4π ≈ 12.6 cm
area = π(9²) × 80/360 = 18π ≈ 56.5 cm²
perimeter = 4π + 18 ≈ 30.6 cmFor the whole topic, read Arcs, sectors and mensuration: key points, common mistakes and how the DSE tests it.