Question

The area of a sector of a circle with a central angle of 75° is 12cm. Find the radius of the circle.

Do not round any intermediate computations. Round your answer to the nearest tenth.

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\\ A=12\\ \theta =75 \end{cases}\implies 12=\cfrac{(75)\pi r^2}{360}\implies 12=\cfrac{5\pi r^2}{24} \\\\\\ 288=5\pi r^2\implies \cfrac{288}{5\pi }=r^2\implies \sqrt{\cfrac{288}{5\pi }}=r\implies 4.3\approx r`