A tank has the shape of an inverted circular cone with heigh

A tank has the shape of an inverted circular cone with heightH=16m and base radiusR=3m. The tank is initially full of water. Find the work required to lower the height of the water level toh=7m by pumping the water to the top of the tank.

Each particle in the layerLxmust travel the distancex. The workW(x)done to raiseLxto the top is the product of the forceFxand the distancex:

Solution

r=R(H-x)/H dV=pi^r^2dx =piR^2/H^2*(H-x)^2dx dm=dV*1000 dW=xdmg W=4580889.398 J