Given, sector area, A=5π.
The radius of the circle, r=6 in.
The sector area can be expressed as,
[tex]\begin{gathered} A=\frac{1}{2}r^2\times\theta \\ \text{Here, }\theta\text{ is the central angle in radians.} \end{gathered}[/tex]Put A=5π, r=6 in in the above equation to find the central angle.
[tex]\begin{gathered} 5\pi=\frac{1}{2}\times6^2\times\theta \\ 5\pi=\frac{1}{2}\times36\times\theta \\ \frac{5\pi\times2}{36}=\theta \\ \frac{10\pi}{36}=\theta \\ \frac{5\pi}{18}=\theta \end{gathered}[/tex]Therefore, the central angle is equal to 5π/18.
