# Math Help - Circumference to area

1. ## Circumference 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.

2. $Area = \pi r^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$
$Circumference = 2 \pi r \ \ (2)$

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

you put this into the formula for the circumference.

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

bring the $2 \pi$ into the root.

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

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