If I know the area of a circle I know that I can find the circumference of the circle by the formula C=Sqrt(4 Pi A) where A is the area of the given circle. My question is where does this formula come from? Thank you.

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- Mar 23rd 2008, 09:15 AMschinb64Circumference to area
If I know the area of a circle I know that I can find the circumference of the circle by the formula C=Sqrt(4 Pi A) where A is the area of the given circle. My question is where does this formula come from? Thank you.

- Mar 23rd 2008, 09:46 AMbobak
$\displaystyle Area = \pi r^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$

$\displaystyle Circumference = 2 \pi r \ \ (2)$

using $\displaystyle (1)$ we have $\displaystyle r = \sqrt{\frac{A}{\pi}}$

you put this into the formula for the circumference.

$\displaystyle C = 2\pi \sqrt{\frac{A}{\pi}} $

bring the $\displaystyle 2 \pi$ into the root.

$\displaystyle C = \sqrt{\frac{4\pi^{\not{2}^{~1}} A}{\not{\pi}}} $

cancel down to get $\displaystyle C = \sqrt{4 \pi A} $