Note that we could move A to B and have concentric circles
The radius of the larger circle = 8
We are looking for this
Area of circle B - area of circle A = shaded area
And
Shaded area = 8 * area of circle A....so
Area of circle B - area of circle A = 8 * area ofcircle A
Area of circle B = 9 * area of circle A
pi * 8^2 = 9 *pi * r^2 where r is the radius of circle A
64 = 9 r^2
64/9 = r^2 take the positive root of both sides
8 / 3 cm = r = radius of smaller circle A
So....the diameter of circle A = 2 (8/3) = 16 / 3 cm