Question

The circumference of a circle is 11n inches. What is the area end square inches of the circle express your answer in terms of n show your show your work

Answer 1

`\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=11n \end{cases}\implies 11n=2\pi r\implies \cfrac{11n}{2\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill`

`\bf \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies A=\pi \left( \boxed{\cfrac{11n}{2\pi }} \right)^2\implies A=~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot \cfrac{11^2 n^2}{2^2 \underset{\pi }{~~\begin{matrix} \pi^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A=\cfrac{121n^2}{4\pi }~\hfill`