# Calculus Work Problem (Spherical Water Tower)

1. Dec 19, 2008

### dbai

1. The problem statement, all variables and given/known data

A spherical water tower 40 ft in diameter has its center 120 ft above the ground. That means, there is a 120 ft pole connected to the 40 ft diameter spherical tank. Water is being pumped at the ground level to fill the tank with water of density 62.4 lb/ft3,

a) How much work is done in filling the tank half full?
b) How much work is done in filling the tank ENTIRELY full?

2. Relevant equations

dW = (dV)*(density)*(displacement)

3. The attempt at a solution

• I calculated that dV would be a cylindrical section of the tank with height dy --> πx2 dy
• Density is given 62.4 lb/ft3
• I used (120 - y) as my displacement

∫(Pi)x2(120 - y) dy Limits: 0-120 ??

I don't know if the displacement is correct and how to convert x in terms of y.

2. Dec 19, 2008