Question

What is the area of a 30 degree sector of a circle with area 96 pi meters ^2?

Answer 1

$\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=96\pi \end{cases}\implies 96\pi =\pi r^2 \\\\\\ \cfrac{96\underline{\pi }}{\underline{\pi }}=r^2\implies 96=r^2\implies \boxed{\sqrt{96}=r}\\\\ -------------------------------$

$\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta = angle~in\\ \qquad degrees\\ ------\\ \theta =30\\ r=\boxed{\sqrt{96}} \end{cases}\implies A=\cfrac{(30)(\pi )(\sqrt{96})^2}{360} \\\\\\ A=\cfrac{(30)(\pi )(96)}{360}\implies A=8\pi$