How to Find the Circumference of a Circle

Geometry · Circles and area

How to Find the Circumference of a Circle

Problem

r = 7

Answer

C = 14\pi \approx 44.0

Circumference is the perimeter of a circle. It is a little more than three times the diameter, and the formula C = 2 pi r makes that exact.

Step-by-step solution

Write the circumference formula.
$C = 2\pi r$
Why: The circumference is the distance around the circle.
Substitute the radius.
$C = 2\pi(7)$
Why: The radius is 7.
Multiply to get the exact answer.
$C = 14\pi$
Why: Keep pi in the answer for an exact value.
Estimate with pi about 3.14.
$14 \times 3.14 \approx 44.0$
Why: The estimate checks the size of the exact answer.

Common mistakes

Using the diameter in place of the radius. That doubles the answer.
Squaring the radius. Circumference uses r, not r squared.
Dropping pi and writing 14. The exact answer keeps pi.

Practice problems

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

$r = 3$

Show answer

$C = 6\pi$
$r = 5$

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$C = 10\pi$
$d = 8$

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$C = 8\pi$
$r = 1$

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$C = 2\pi$
$d = 20$

Show answer

$C = 20\pi$