Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.

A spherical water tank, 24 ft in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long will it take to fill the tank? (One horsepower − 550 ft-lb of work per second.)