Circles: Area, Arc Length and Sector Area
Circle measures depend on the radius, central angle and the value used for π.
Parts and formulas
The radius r is half the diameter. Circumference C = 2πr and area A = πr². For a sector with central angle θ, arc length = θ/360 × 2πr and sector area = θ/360 × πr².
Worked examples
- For r = 7 cm and π = 22/7, circumference = 44 cm and area = 154 cm².
- A 90° sector is one quarter of a circle, so its area is 1/4πr².
- For r = 6 cm and θ = 60°, arc length = 60/360 × 2π × 6 = 2π cm.
Practice
- Find the circumference and area of a circle of radius 5 cm.
- Find the area of a 120° sector with radius 3 cm.
- Find the arc length of a 45° sector of radius 8 cm.
