Question

What is the radius of the circle if the area is 50π and the angle is 80 degrees?

Answer 1

15

1) Considering that the sector of a circle can be found through the proportion:

$\begin{gathered} 360^{\circ}------\pi\cdot r^2 \\ 80^{\circ}------50\pi \\ 80\cdot\pi\cdot r^2=360\cdot50\pi \\ 80\pi r^2=18000\pi \\ r^2=\frac{18000\pi}{80\pi} \\ r^2=225 \\ \sqrt[]{r^2}=\sqrt[]{225} \\ r=15 \end{gathered}$

Note that, the area of a circle corresponds to 360º and 50pi to 80º in this question. The angle has been given in degrees.

2) SO, the measure of the radius is 15 units