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Math Help - Finding the Volume of a Pool

  1. #1
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    Finding the Volume of a Pool

    Find the Total Volume of a Pool:


    As viewed from above, a swimming pool has the shape of the ellipse


    x^2/900+y^2/400 = 1


    The cross sections perpendicular to the ground and parallel to the y-axis are squares. Find the total volume of the pool. (Assume the units of length and area are feet and square feet respectively. Do not put units in your answer.)
    V =

    how do I do this problem?

    I've tried several different formulations, and I figured the answer was Int (subscript -30, superscript 30) (X^2)-900 dx but this does not appear to be the correct answer.
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  2. #2
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    If we take our pool equation and solve for y we get:

    y=\frac{2}{3}\sqrt{900-x^{2}}

    This is the length of the base of the square as the cross sections stack up along the x-axis.

    But the cross-sections are squares:

    \frac{16}{9}\int_{0}^{30}\left(\sqrt{900-x^{2}}\right)^{2}dx

    We squared our function and multiplied by 4 because the integral gives the area in one quadrant of the ellipse.

    What we end up with is a very easy integral once it is set up.
    Last edited by galactus; November 24th 2008 at 06:38 AM.
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  3. #3
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    That would seem to get me the final answer of 32000, which does not seem to work.

    Am I calculating incorrectly?
    Last edited by Pikeman85; June 23rd 2008 at 06:29 PM.
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