You can model the tank by where the center of the tank is at (0, 0, 0). For a given z between -r and r, we have a thin "sheet" of water covering the disk which has radius so area . Taking the sheet to have "infinitesmal" thickness dz it has volume and so weight where is the density of water in kilograms per meter. To lift that "sheet" to the top of the sphere, you have to lift it r- z meters and then you have to lift it that additional h meters to the outlet. That is you have to lift weight [tex]g\gamma\pi(r^2- z^2)[tex] a distance meters and so have to do work to lift that sheet out of the tank. To find the total work to empty the tank integrate that from z= -r to r.