Question

The area of this circle is 96 m².

What is the area of a 30° sector of this circle?
O 4 pi m²
O 8 pi m²
9 pi m²
O 16 pi m²

Answer 1

`\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=96\pi \end{cases}\implies 96\pi =\pi r^2\implies \cfrac{96\pi }{\pi }=r^2\implies 96=r^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r^2=96\\ \theta =30 \end{cases}\implies A=\cfrac{(30)\pi (96)}{360}\implies {\Large \begin{array}{llll} A=8\pi \end{array}} ~m^2`