CIR006 · Circles · Classes 7–9
Central angles
A central angle has its vertex at the centre. The arc and the sector it cuts off are the same fraction θ/360 of the whole circle.
∠AOBCentral angles
📐 Formula
arc = (θ/360) × 2πr; sector = (θ/360) × πr²
✏️ Worked example
r = 6, θ = 60°: arc = 2π ≈ 6.28, sector area = 6π ≈ 18.85.
🌍 Where it is used
Pie charts, clock hands, pizza slices.
❓ Quick check
Central angles around a point add to…
🏋️ Practice
EasyFraction of a circle for 90°?
Answer: ¼
MediumPie chart: 25% of the data. Angle?
Answer: 90°
ChallengeArc of 120° in a circle of radius 3?
Answer: 2π ≈ 6.28