Surface Integrals, Stokes & Divergence · Hard problem

A conical storage tank, vertex at the bottom, has a flat circular top of radius $3$ m at height $h$. Engineers model the tank's internal expansion with the field $\mathbf F = (x, y, z)$ and, using the divergence theorem, measure the total outward flux of $\mathbf F$ through the tank's whole surface (the slanted wall together with the flat top) to be $81\pi$ m$^3$/s. Find the height $h$, in meters.