Question

12

Calculate the area of the given segment. Round your answer to the nearest tenth, if necessary.
60
8 in.

Answer 1

Check the picture below.

`\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{√(3)}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16√(3)\implies A\approx 5.8~in^2`