Surface Integrals, Stokes & Divergence · Hard problem

A spherical fuel tank of radius $3$ m has a circular hatch cut out at the top, where $z\ge1$. Seepage is modeled by the radial field $\mathbf F=(x,y,z)$ (m/day). Find the outward flux of $\mathbf F$ through just the remaining tank surface (the sphere with the hatch's cap removed).