I'm assuming here that the small circle touches the medium circle like so
(a) The radius of the medium circle = (6 + 10) / 2 = 8
(b) The area of the medium circle = pi * 8^2 = 64 pi
The area of Z = area of large circle - area of medium circle = (10^2 - 8^2) pi = 36pi ≈ 113.1 cm^2
(c) The area of the small circle = Y = pi * 6^2 = 36pi
X is the area between the medium circle and the small circle = (8.^2 - 6^2) pi
So Y / X = 36 / [ (8^2 - 6^2) ] = 36/28 = 9 / 7