How to Find the Radius from the Circumference

Problem

C = 20\pi

Answer

r = 10

Rearranging a formula is solving a one-step equation. Divide the circumference by 2 pi, and the pi cancels when the circumference is a multiple of pi.

Step-by-step solution

Write the circumference formula.
$C = 2\pi r$
Why: The formula links the circumference to the radius.
Substitute the known circumference.
$20\pi = 2\pi r$
Why: Both sides now use the same units.
Divide both sides by 2 pi.
$r = \frac{20\pi}{2\pi} = 10$
Why: Pi cancels, leaving the radius alone.

Common mistakes

Dividing by 2 only and writing 10 pi.
Answering with the diameter. The formula gives the radius directly.
Keeping pi in the answer. The pi divided out.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$C = 12\pi$

Show answer

$r = 6$
$C = 6\pi$

Show answer

$r = 3$
$C = 30\pi$

Show answer

$r = 15$
$C = 8\pi$

Show answer

$r = 4$
$C = 50\pi$

Show answer

$r = 25$