I was not sure if it fits better here, or in the math forum, but this is the problem I am trying to solve:

Say you have a full cylinder of radius $R$, height $L$, and its uniformly charged with volume density $\rho$. And now I draw a hollow cylinder inside (with the same height, and radius $r < R\,$), is there any numerical relationship between its surface density $\sigma$(r) and $\rho$ ?

Thanks in advance.