Maths · Geometry & Measures
Circles: circumference & area
Use π formulas for circles.
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What is π?
The number π (pi) is about 3.14159. It shows how a circle's circumference compares to its diameter. Every circle, big or small, has the same π ratio.
Circumference of a Circle
Circumference is the distance around a circle. The formula is C = πd or C = 2πr. Here d is diameter and r is radius.
Area of a Circle
Area is the space inside a circle. The formula is A = πr². You square the radius, then multiply by π.
Radius and Diameter
The radius is the distance from the centre to the edge. The diameter goes all the way across through the centre. Diameter = 2 × radius.
Using π in Calculations
You can leave π as a symbol for exact answers. Or use π ≈ 3.14 for approximate answers. Your teacher will tell you which to use.
Worked examples
1. A circle has radius 5 cm. Find its circumference using π.
- Use the formula C = 2πr.
- Substitute r = 5: C = 2 × π × 5.
- Simplify: C = 10π cm.
2. A circle has diameter 8 m. Find its area using π.
- First find the radius: r = 8 ÷ 2 = 4 m.
- Use the formula A = πr².
- Substitute r = 4: A = π × 4² = π × 16 = 16π m².
3. A circle has radius 3 cm. Find its area using π ≈ 3.14.
- Use A = πr² with r = 3.
- A = 3.14 × 3² = 3.14 × 9.
- A = 28.26 cm².
Try it yourself
A circle has radius 6 cm. Find its circumference in terms of π.
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