Change of variables needed?

Let there be a surface bounded below by the cone and above by . Calculate the flux through this surface due to a vector field **F**(x, y, z), whose divergence cleanly works out to be 2z.

This turns out to be a triple integral BUT I'm not sure if I should integrate 2z or 2z*r, with the r coming from changing coordinate systems from rectangular to polar. I don't know if I'm even supposed to be changing coordinate systems since z is a polar coordinate. Do I need to treat this as if I changed variables, or should I just plainly integrate 2z?

Thanks

Anthony