A sector has an angle of 64 and an area of 10pi cm2

Asector  = (1/2)r^2(theta)    where theta is in radian measure.....so we have

10pi cm^2 = (1/2)r^2 ( 64 * pi / 180)  =     divide both sides by pi, multiply both sides by 2

20 cm^2   = r^2 (64/180)     multiply both sides by  180/64

[ 180 * 20 / 64] cm^2  = r^2       take the sqrt of both sides

r = 7.5 cm  ...and this is the radius

Here's the picture of your circle......the area of 31.24 cm^2 ≈  10pi cm^2.......the radius = 7.5