Circles • Topic 3 of 7

Circumference

The circumference is the distance around a circle — its perimeter. It is found with C = 2πr, or equivalently C = πd. The SAT usually wants the answer left in terms of π (for example 10π) rather than as a decimal, which keeps it exact. Given the radius, double it and attach π; given the diameter, just attach π. You can also work backward: if the circumference is 12π, then 2πr = 12π gives r = 6. Don’t confuse circumference (distance around, uses 2πr) with area (space inside, uses πr²) — picking the wrong formula is the most common slip.

A circle with its outline highlighted and a radius labelled rCircumferencerC = 2πr

✅ Solved examples

1. A circle has radius 6. Find its circumference in terms of π.
C = 2πr = 2π(6) = 12π.
2. A circle has radius 10. Find its circumference.
2π(10) = 20π.
3. A circle has diameter 8. Find its circumference.
C = πd = 8π.
4. A circle has circumference 14π. Find its radius.
2πr = 14π, so r = 7.

✏️ Practice — try these, take hints as needed

1. A circle has radius 9. Find its circumference in terms of π.
C = 2πr.
2π(9).
—
18π.
2. A circle has radius 12. Find its circumference.
2π(12).
—
—
24π.
3. A circle has diameter 5. Find its circumference.
C = πd.
—
—
5π.
4. A circle has circumference 20π. Find its radius.
2πr = 20π.
r = 20 ÷ 2.
—
10.
5. A circle has radius 2. Find its circumference.
2π(2).
—
—
4π.

📝 Topic test — 8 questions

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