Answer
45,000 ft-lbs
Work Step by Step
find volume of slice
delta V = 10 * (-2x+12) * delta x ft3
find force, use p = 62.5 lb/ft3
delta F = p * delta V = 62.5 lb/ft3 * 10 * (-2x+12) * delta x ft3
find work
delta W = delta F * d = 625 lb (-2x+12) * delta x * (x-0) ft-lbs
take integral for work
W = 625 \int from 0 to 6 x(-2x+12) dx
= 45,000 ft-lbs
