A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle?
so if a 83 degree sector of a circle has an area of 60 pi, then we can find some ratios. 83/360 = 60pi/ (area of cricle) so the area of the cirlc ewould be 21600/83 pi so the radius of the circle would be 60sqrt6 / sqrt83 or 60√49883.
Area = pi r^2 * (83/360)
60 pi = pi* r^2 * (83/360)
r^2 = (60 * 360) / 83
r = sqrt [ 60 * 360 / 83 ] ≈ 16.13