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Calculus Work Problem (Spherical Water Tower)

  1. Dec 19, 2008 #1
    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. jcsd
  3. Dec 19, 2008 #2
    I am not sure what it is are using x for? Do you mean r?
  4. Dec 19, 2008 #3


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    Homework Helper

    What is x supposed to be here? You should draw a picture of a right-angle triangle whose L-shape rests upright on the infinitesimal cylindrical slice of water. Then the hypotenuse would be constant, namely 20^2. Denote the base by x (or r) and the height as 20-y. See how to take to it from here?
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