Therefore: [ W = 196000 \left( \frac27\pi4 + 9 \right) \quad \textJoules. ]

His foreman yelled, “Rico, how much work will the pump do? We need to budget for fuel!”

[ dW = \textforce \times \textdistance = 196000\sqrt9-y^2 \cdot (3 - y) , dy. ]

The water filled from the bottom ((y = -3)) up to the center line ((y = 0)), so half-full.

Rico remembered Ricardo Asin’s golden rule: “For work problems, slice it, find the force on each slice, multiply by the distance that slice travels, then integrate.”

Rico told the foreman, “About 5.9 megajoules.” The foreman nodded, and the pump worked perfectly—thanks to a slice, a distance, and an integral from page 54 of Ricardo Asin’s reviewer.