Chapter 6.7, Problem 12E

Consider the cylindrical tank in Example 4 that has a height of 10 m and a radius of 5 m. Recall that if the tank is full of water, then ${\displaystyle {\int }_0^{10}25\pi \rho g\left(15-y\right)dy}$ equals the work required to pump all the water out of the tank, through an outflow pipe that is 15 m above the bottom of the tank. Revise this work integral for the following scenarios. (Do not evaluate the integrals.)

12.    The work required to empty the tank if the water in the tank is only 3 m deep and the outflow pipe is at the top of the tank