Question

Given that an intercepted arc has length 6pi inches and a central angle is pi/3, find the radius

Answer 1

`\bf \textit{arc's length}\\\\ s=r\theta \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ s=6\pi \\ \theta =(\pi )/(3) \end{cases}\implies 6\pi =r\left( (\pi )/(3) \right)\implies \cfrac{6\pi }{(\pi )/(3)}=r \\\\\\ \cfrac{6\pi }{1}\cdot \cfrac{3}{\pi }=r\implies 18=r`