Question

If the radius of a sector is 8 inches and the central angle of the sector is 40, find the area of the sector.

Answer 1

22.34 in^2 to the nearest hundredth.

Explanation:

Area = π r^2 * 40/360

= π * 8^2 * 1/9

= 7.111π

= 22.3402 in^2.

Answer 2

`\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=8\\ \theta =40 \end{cases}\implies A=\cfrac{(40)\pi (8)^2}{360} \\\\\\ A=\cfrac{64\pi }{9}\implies A\approx 22.34~in^2`