Question

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

Answer 1

first, notice that angles POS and ROS are supplementary, then:

$\begin{gathered} \angle POS+\angle ROS=180 \\ \Rightarrow45+\angle ROS=180 \\ \Rightarrow\angle ROS=180-45=135 \\ \angle ROS=135\degree \end{gathered}$

then, we can use the equation of the area of a circle sector:

$A_s=\frac{\theta\pi}{360}\cdot r^2$

in this case, we have that the diameter is RP = 8, then the radius is r = RP/2 = 4, then, using the formula and knowing that the angle of the shaded area measures 135 degrees, we get:

$\begin{gathered} \theta=135 \\ r=4 \\ \Rightarrow A_s=\frac{135(3.1416)}{360}\cdot(4)^2=18.85 \\ A_s=18.85 \end{gathered}$

therefore, the area of the shaded sector is 18.85 square units