Question

A round mirror has a circumference of 87.92 inches. Calculate the area of the mirror.

Answer 1

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=87.92 \end{cases}\implies 87.92=2\pi r\implies \cfrac{87.92}{2\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2~\hspace{7em}A=\pi \left( \boxed{\frac{87.92}{2\pi }} \right)^2 \\\\\\ A=\pi \cdot \cfrac{87.92^2}{4\pi^2}\implies A=\cfrac{87.92^2}{4\pi }\implies A\approx 615.127998$