A spherical tank with radius of 5 feet is set on a coloumn 15 feet above the ground. How much work is required to fill the tank with water if the solution is pumped from ground level?

Answer 1

Let the center of the tank be at (0,0)

when the water level is at y, the radius of the water surface is

r^2 = 25-y^2

Work is ∫F(y) dy

F(y) is the weight of the water. So, since each slice of water in the tank is raised 21+y feet, and water weighs 62.4 lbs/ft^3,

W(y) = ∫[-5,5] 62.4 π (25-y^2) (21+y) dy
= 218400π