Circles • Topic 1 of 4

Radius, Diameter, Circumference

The radius (r) runs from the centre to the edge; the diameter (d) crosses the full circle through the centre, so d = 2r. The circumference — the distance around the circle — is C = 2πr, equivalently πd. Every circle question starts by pinning down the radius, because circumference and area both flow from it. The GRE usually wants the answer left as a multiple of π (for example 14π rather than 43.98), which is both faster and exact. Reverse questions are common: given the circumference, divide by 2π to recover the radius. Watch the wording carefully — mixing up radius and diameter is the most common way to double or halve an answer by mistake.

A circle with centre O, a radius and a diameterRadius, diameter, circumferenceOdrC = 2πr = πd

✅ Solved examples

1. A circle has a radius of 7. Find its circumference.
C = 2πr = 2π × 7 = 14π.
2. A circle has a diameter of 10. Find its circumference.
C = πd = π × 10 = 10π.
3. A circle has a circumference of 12π. Find its radius.
C = 2πr → 12π = 2πr → r = 6.
4. Quantitative Comparison. Circle X has radius 5; circle Y has diameter 8. Quantity A: circumference of X. Quantity B: circumference of Y. Which is greater?
X: C = 2π × 5 = 10π. Y: C = π × 8 = 8π. Since 10π > 8π, Quantity A is greater. (The trap is comparing 5 with 8 directly and picking Y.)

✏️ Practice — try these, take hints as needed

1. A circle has a radius of 5. Find its circumference.
C = 2πr.
2π × 5.
Leave in terms of π.
10π
2. A circle has a diameter of 14. Find its circumference.
C = πd.
π × 14.
No need to halve.
14π
3. A circle has a circumference of 20π. Find its diameter.
C = πd.
20π = πd.
Divide by π.
20
4. A circle has a radius of 3. Find its diameter.
d = 2r.
2 × 3.
Simple doubling.
6
5. A circle has a circumference of 8π. Find its radius.
C = 2πr.
8π = 2πr.
Divide by 2π.
4

📝 Topic test — 8 questions

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