Circles • Topic 2 of 4

Area of a Circle

The area enclosed by a circle is A = πr². Because the radius is squared, area grows much faster than circumference: double the radius and the circumference doubles, but the area quadruples — a favourite Quantitative Comparison hook. If the problem gives the diameter, halve it first; forgetting to do so is the classic error that inflates the area fourfold. Reverse questions divide by π and take a square root: an area of 49π means r² = 49, so r = 7. Keep answers in terms of π unless a decimal is explicitly required, and be alert to composite figures where a circle is inscribed in a square or a smaller circle is removed from a larger one.

A shaded circle with a radius drawn, showing its areaArea of a circlerArea = πr²

✅ Solved examples

1. A circle has a radius of 5. Find its area.
A = πr² = π × 5² = 25π.
2. A circle has a diameter of 12. Find its area.
Radius = 12 / 2 = 6, so A = π × 6² = 36π.
3. A circle has an area of 49π. Find its radius.
πr² = 49π → r² = 49 → r = 7.
4. A circle has an area of 16π. Find its diameter.
r² = 16 → r = 4, so diameter = 2 × 4 = 8.

✏️ Practice — try these, take hints as needed

1. A circle has a radius of 3. Find its area.
A = πr².
π × 3².
3² = 9.
9π
2. A circle has a diameter of 10. Find its area.
Halve the diameter first.
r = 5.
A = π × 25.
25π
3. A circle has an area of 64π. Find its radius.
r² = 64.
Take the square root.
√64.
8
4. A circle has an area of 100π. Find its diameter.
r² = 100 → r = 10.
Diameter = 2r.
2 × 10.
20
5. A circle has a radius of 7. Find its area.
A = πr².
7² = 49.
Multiply by π.
49π

📝 Topic test — 8 questions

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