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Math Help - green's theorem

  1. #1
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    green's theorem

    How do i do this pls?
    Find the volume of the greatest rectangular parallelopiped that can be inscribed in the ellipsoid:
    x^2/a^2+y^2/b^2+z^2/c^2=1
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  2. #2
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    Quote Originally Posted by shushu View Post
    How do i do this pls?
    Find the volume of the greatest rectangular parallelopiped that can be inscribed in the ellipsoid:
    x^2/a^2+y^2/b^2+z^2/c^2=1
    Are you allowed to assume that the largrest such parallelopiped has edges parallel to the axes? If so, then if a vertex in the first octant is (x,y,z) the eges have length 2x, 2y, and 2z. Maximize V= 8xyz subject to the constraint that \frac{x^2}{a^2}+ \frac{y^2}{b^2}+ \frac{z^2}{c^2}= 1.

    Was there a reason for titling this "Green's theorem"? It doesn't seem to have anything to do with Green's theorem.
    Last edited by HallsofIvy; April 4th 2010 at 06:56 AM.
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