Circles • Topic 2 of 7

Diameter

The diameter is the distance across a circle through its centre — the longest chord — and it equals twice the radius: d = 2r. Equivalently, the radius is half the diameter. The circumference can be written either as 2πr or as πd, so the diameter gives a quick route to circumference. Diameter problems are usually direct conversions: double the radius, or halve the diameter to get the radius before using an area or circumference formula. The SAT often states a diameter and expects you to convert to a radius first, since the area formula needs r, not d. Keep the factor of two straight.

A circle with a diameter drawn through the centreDiameterdd = 2r

✅ Solved examples

1. A circle has radius 8. Find its diameter.
2 × 8 = 16.
2. A circle has diameter 14. Find its radius.
14 ÷ 2 = 7.
3. A circle has diameter 10. Find its circumference in terms of π.
C = πd = 10π.
4. A circle has radius 11. Find its diameter.
2 × 11 = 22.

✏️ Practice — try these, take hints as needed

1. A circle has radius 15. Find its diameter.
d = 2r.
2 × 15.
—
30.
2. A circle has diameter 18. Find its radius.
r = d ÷ 2.
18 ÷ 2.
—
9.
3. A circle has diameter 6. Find its circumference in terms of π.
C = πd.
—
—
6π.
4. A circle has radius 21. Find its diameter.
2 × 21.
—
—
42.
5. A circle has diameter 24. Find its radius.
24 ÷ 2.
—
—
12.

📝 Topic test — 8 questions

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