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{√(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{√(96)} \end{cases}\implies A=\cfrac{(30)(\pi )(√(96))^2}{360} \\\\\\ A=\cfrac{(30)(\pi )(96)}{360}\implies A=8\pi`