Question

The sector of a circle has an area of 104π/9 square inches and a central angle with measure 65° What is the radius of the circle, in inches?

A- 104 in
B- 64 in
C- 5.7 in
D- 8 in

Answer 1

`\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\\ \theta =65\\ A=(104\pi )/(9) \end{cases}\implies \cfrac{104\pi }{9}=\cfrac{(65)\pi r^2}{360}\implies \cfrac{104\pi }{9}=\cfrac{13\pi r^2}{72} \\\\\\ \cfrac{72}{13\pi}\cdot \cfrac{104\pi }{9}=r^2\implies 64=r^2\implies √(64)=r\implies \boxed{8=r}`