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Math Help - Work: The Pool Problem

  1. #1
    Member RedBarchetta's Avatar
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    Work: The Pool Problem

    1. The problem statement, all variables and given/known data
    A circular swimming pool has a diameter of 22 ft, the sides are 5 ft high, and the depth of the water is 4 ft. How much work is required to pump all of the water over the side? (Use the fact that water weighs 62.5 lb/ft^3.)

    (a) Show how to approximate the required work by a Riemann sum. Give your answer using the form below. (If you need to enter -infinity or infinity, type -INFINITY or INFINITY.)


    (b)Express the work as an integral and evaluate it.

    3. The attempt at a solution
    I've found everything in the riemann sum equation minus the "E". What would this be?
    A=N
    B=infinity
    C=1
    D=N
    E=?

    One I find that, I should be able to setup the integral and solve it.

    Thanks!
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    The kth layer is a cylinder of radius 11 and height {\Delta}x_{k}

    the force required to move it is ({\pi}r^{2}{\Delta}x_{k})\cdot[\text{weigth density of water}]

    The work needed to pump the kth layer of the edge of the pool would be

    W_{k}=(5-x_{k})\cdot{62.5{\pi}(121)}{\Delta{x_{k}}}

    \frac{15125\pi}{2}\int_{0}^{4}(5-x)dx
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  3. #3
    Member RedBarchetta's Avatar
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    So what is E in the reimann sum? I've entered everything, but came up with no correct answer.

    Thank you Galactus, you explain the problem so it actually makes sense!
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