To answer this question we will use the following formula to compute the area of a sector with central angle x degrees and radius r:
[tex]Area=\frac{\pi r^2\times x}{360}.[/tex]
Since RP is a diameter, then:
[tex]m\angle ROS+m\angle SOP=180^{\circ}.[/tex]
Then:
[tex]m\angle ROS=135^{\circ}.[/tex]
Therefore the area of sector ROS is:
[tex]Area=\frac{\pi\times8^2\times135}{360}.[/tex]
Simplifying the above result we get:
[tex]Area=24\pi.[/tex]
Answer: Option c.
