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Math Help - Help with volume formula

  1. #1
    Newbie
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    Aug 2010
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    Help with volume formula

    The volume of water a spherical tank can hold is given by the next formula:

    V(h)= \pi h^2 \frac{3R - h}{3}

    , where:

    ● V is the water volume inside the tank in m^3
    ● R is the radius in m, and
    ● h is the level of water, measured from the bottom of the tank (in m^3).

    I need to find out, using bisection and Newton-Raphson iterations, what the level of water has to be in order to get 90m^3 of water from a 3m radius tank.

    So basically, what i've done is find the value of h within the formula, and apply bisection to the resulting equation. But here's the problem. The resulting formula is a 3 degree formula, so i get 3 roots (obviously bisection gives me just one, depending on the initial interval).

    So the three roots are (aprox.):
    7.4526264
    4.2565863
    - 2.7092127

    Thanks in advance.

    P.S.: I'm using scilab as my numerical analysis software.
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  2. #2
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
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    What is your question? It looks like you have the solution right there.
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  3. #3
    Newbie
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    Aug 2010
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    Sorry, stupid me.. the tank is 3m in radius, so the 7.54(something) root is irrelevant.

    Thanks anyways.
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