Question

Find the radius of the circle given the central angle and the area of the Shaded sector

Answer 1

we have the following formula for the area of a sector of a circle:

`A_s=(\theta\cdot\pi)/(360)\cdot r^2_{}`

In this case, we have the following information:

`\begin{gathered} A_s=60\pi \\ \theta=24\degree \end{gathered}`

then, using the formula and solving for r, we get the following:

`\begin{gathered} 60\pi=(24\cdot\pi)/(360)\cdot r^2 \\ \Rightarrow360\cdot60\pi=24\pi\cdot r^2 \\ \Rightarrow21600\pi=24\pi\cdot r^2 \\ \Rightarrow r^2=(21600\pi)/(24\pi)=900 \\ \Rightarrow r=\sqrt[]{900}=30 \\ r=30 \end{gathered}`

therefore, the measure of the radius is r = 30