Question

A circle for a game spinner is divided into 3 regions as shown. RP is a diameter. What is the area of the shaded sector ROS if RP=8

Answer 1

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:

`Area=(\pi r^2* x)/(360).`

Since RP is a diameter, then:

`m\angle ROS+m\angle SOP=180^(\circ).`

Then:

`m\angle ROS=135^(\circ).`

Therefore the area of sector ROS is:

`Area=(\pi*8^2*135)/(360).`

Simplifying the above result we get:

`Area=24\pi.`

Answer: Option c.