Chapter 6.7, Problem 9E

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.)

9.    The work required to empty the top half of the tank