Find the work

Question

A tank is full of water. Find the work required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Assume r = 6 ft, R = 12 ft, and h = 20 ft.)

Answer 1

Work required is Weight*distance.

We have a conical tank, so at height y, the radius r(y) = r + y(R-r)/h; r(y)= 6+3y/10; the slice height is dy, so the weight of this slice is π r(y)²*dy = π (6+3y/10)²*dy; the distance is 20-y;

The total works W= ∫₀^h Weight*distance = ∫₀^h π (r + y(R-r)/h)² (20-y) dy

W = 825000 π ft*lb