A cylindrical water tank has a radius of 4 feet and a height of 3.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft³.] A) 14,115 ft-lbs B) 4705 ft-lbs C) 281 ft-lbs D) 7390 ft-lbs

Question

Quizplus · Accepted Answer

The work done to pump the water out is calculated by integrating the weight of each infinitesimally thin horizontal slice of water times the distance it needs to be lifted. The volume of the tank is πr²h = π(4)²(3) = 48π ft³. The weight of the water is 48π * 62.4 lbs. The center of mass of the water is at 1.5 feet, so the work done is 48π * 62.4 * 1.5 = 14,115 ft-lbs.

A Cylindrical Water Tank Has a Radius of 4 Feet