Question

Find the circumference of a circle whose area is 24 pi ft ^2

Answer 1

$\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=24\pi \end{cases}\implies 24\pi =\pi r^2\implies \cfrac{24\pi }{\pi }=r^2 \\\\\\ 24=r^2\implies \boxed{\sqrt{24}=r}\\\\ -------------------------------\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \implies C=2\pi\left( \boxed{\sqrt{24}} \right)~~ \begin{cases} 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 6 \end{cases} \\\\\\ C=2\pi \sqrt{2^2\cdot 6}\implies C=2\pi (2\sqrt{6})\implies C=4\sqrt{6}~\pi$