Circles • Topic 1 of 7

Radius

The radius is the distance from the centre of a circle to any point on it, and it is the key measurement from which every other circle quantity is built. The diameter is twice the radius, the circumference is 2πr, and the area is πr². So once you know the radius you can find everything else. Conversely, if you are given the area or circumference you can work back to the radius. The SAT frequently asks for the area given the radius (πr²) or expects you to recover the radius from another measure, so keep the relationships d = 2r, C = 2πr and A = πr² ready.

A circle with its centre O and a radius drawn to the edgeRadiusOrArea = πr²

✅ Solved examples

1. A circle has radius 5. Find its area in terms of π.
A = πr² = π(5)² = 25π.
2. A circle has radius 3. Find its area.
π(3)² = 9π.
3. A circle has radius 10. Find its diameter.
2 × 10 = 20.
4. A circle has area 36π. Find its radius.
r² = 36, so r = 6.

✏️ Practice — try these, take hints as needed

1. A circle has radius 7. Find its area in terms of π.
A = πr².
π(7)².
—
49π.
2. A circle has radius 4. Find its area.
π(4)².
—
—
16π.
3. A circle has radius 9. Find its diameter.
d = 2r.
2 × 9.
—
18.
4. A circle has area 25π. Find its radius.
r² = 25.
√25.
—
5.
5. A circle has radius 6. Find its area.
π(6)².
—
—
36π.

📝 Topic test — 8 questions

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