Hey azzarules.

You already have given that dh/dt is proportional to pi*r(t)^2 so if you can express r(t) in terms of h(t) then you have dh/dt = A*pi*r(t)^2 and then solve for h(t) and use the boundary value (time = 20, height = 19.7) to solve for the constant A.

What you had is right except proportionality means you need to include a constant (I've called it A in my post).