A trough is 3 meters long, 1 meters wide, and 3 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 3 meters, and base, on top, of length 1 meters). The trough is full of water (density $1000 kg/m^3$ ). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use $g=9.8 m/s^2$ as the acceleration due to gravity.)