Area of sector = x*pi*r^2 ("x" is a fraction that corresponds to the fraction of the circle made up by the sector)
Central angle = x*2*pi*r ("x" is the fraction of the circle included in the central angle - this also corresponds to the fraction of the circumference that makes up the arc length of the central angle)
x*pi*r^2 = 64pi/5
x*2*pi*r = 8pi/5
You have a system of equations - Two equations and two unknowns.
Since we don't really care what x is equal to, we can just solve each of the above equations for x, and then set the results equal to each other. This yields:
4/(5r) = 64/(5r^2)
Solving this for r yields r = 16.
Thus, the area of the circle is pi*r^2 = 256pi.
