Circumference
The circumference is the distance all the way around a circle. It is found using the special number π (pi), which is about 3.142 or 22/7. The circumference C depends on the radius r or diameter d.
Key idea / Key idea
Circumference: C = 2πr = πd.
Area: A = πr².
Use π ≈ 3.142 or 22/7 as told in the question.
Area of a circle
The area is the amount of surface inside the circle, measured in square units. The formula is A = πr². Always use the radius, not the diameter — if you are given the diameter, halve it first.
Worked example / Worked example
A circle has radius 7 cm. Using π = 22/7, find the circumference and area.
C = 2πr = 2 × (22/7) × 7 = 2 × 22 = 44 cm.
A = πr² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm².
Arcs and sectors
An arc is a fraction of the circumference and a sector is a fraction of the area. If the angle at the centre is θ, the fraction is θ/360°.
Worked example / Worked example
Find the arc length of a sector with angle 90° in a circle of radius 14 cm (π = 22/7).
Arc = (90/360) × 2πr = (1/4) × 2 × (22/7) × 14 = (1/4) × 88 = 22 cm.
Remember / Remember
- C = 2πr = πd; A = πr².
- Area uses radius squared.
- Arc = (θ/360°) × 2πr.
- Sector area = (θ/360°) × πr².