Question

Find the circumference

Answer 1

`\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =87\\ s=14 \end{cases}\implies 14=\cfrac{\pi (87)r}{180} \\\\\\ 2520=87\pi r \implies \cfrac{2520}{87\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill`

`\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \implies C=2~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \left(\boxed{\cfrac{2520}{87~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} \right)\implies C = \cfrac{5040}{87} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill C\approx 57.93~\hfill`