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Surface area of an ellipsoid

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  • Surface area of an ellipsoid

    Dear Fellow Biomechanicians,

    Can anyone help with this problem? I need to calculate
    the surface area of an ellipsoid whose defining equation is:

    2 2 2
    X Y Z
    ---- + ---- + ---- = 1
    2 2 2
    a b c

    I need the solution for the case where a, b, and c are all
    different, and for the special case where b = c. I also need to
    be able to calculate the surface area for a sector of an
    ellipsoid (i.e., a hemi-ellipsoid or less, but symmetric about
    one of the axes).

    I have seen a paper where both of these solutions are given
    (and they are complex), yet when I try to derive them myself, I
    get different answers, even when using a symbolic algebra
    program. I would appreciate seeing a total derivation.

    In my first try, I got the area equal to:

    4 2 2 2
    --- * pi * (a + b + c )

    This seems intuitively obvious (i.e., if a = b = c you get
    the correct equation for the surface area of a sphere) but
    apparently is NOT correct. I found my error that led to this
    solution, but still have had little luck getting the correct

    I would appreciate any input into this problem. I will
    post all replies at a future date.

    Thanking you in advance,
    --Sandy Stewart
    Research Biomedical Engineer,
    CDRH, Food & Drug Administration