Question

Find the exact area of a circle having the given circumference.

4pi√3
A =
4pi√3
2pi√3
12pi

Answer 1

`\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=4\pi √(3) \end{cases}\implies 4\pi √(3)=2\pi r\implies \cfrac{4\pi √(3)}{2\pi }=r\implies 2√(3)=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2√(3) \end{cases}\implies A=\pi (2√(3))^2 \\\\\\ A=\pi ( ~~ 2^2√(3^2) ~~ )\implies A=\pi ( ~~ 2^2(3) ~~ )\implies A=\implies A=12\pi`