(Solved): (8) (15 pts) An inverted cone creates the tank pictured below. The tank has a height of 12 meters ...

(8) (15 pts) An inverted cone creates the tank pictured below. The tank has a height of 12 meters \( (m) \) and a base diameter of \( 10 \mathrm{~m} \). The tank starts with a depth of \( 9 \mathrm{~m} \) of water. Set up, but do NOT evaluate, the integral needed to determine the work \( W \) required to pump water over the top edge until the depth of the water remaining is \( 1 \mathrm{~m} \). Assume the gravitational constant \( g=9.8 \mathrm{~m} / \mathrm{s}^{2} \) and water density \( \rho=1000 \mathrm{~kg} / \mathrm{m}^{3} \).