Question

The diameter of a circle is 8 kilometers. What is the angle measure of an arc bounding a sector with area 2 pi square kilometers?

Answer 1

\(\bf {\color{red}{ \textit{area of a circle's sector}}}=\cfrac{\theta \pi {\color{blue}{ r}}^2}{360}\quad diameter=8\implies {\color{blue}{ r}} = \frac{diameter}{2}=4
\\ \quad \\
\textit{sector's area is }{\color{red}{ 2\pi}}\qquad thus \qquad {\color{red}{ 2\pi}}=\cfrac{\theta \pi {\color{blue}{ 4}}^2}{360}
\\ \quad \\
\textit{solve for }\theta\)

Answer 2

I got the answer it was 45