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Thread: Help with volume formula

  1. #1
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    Help with volume formula

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

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

    , where:

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

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

    So basically, what i've done is find the value of $\displaystyle h$ 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.):
    ●$\displaystyle 7.4526264$
    ●$\displaystyle 4.2565863$
    ●$\displaystyle - 2.7092127$

    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
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    What is your question? It looks like you have the solution right there.
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  3. #3
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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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