Hi Tom,

The best I can do is to look at an ellipsoid. Even there the surface are is not expressible using standard functions. There is an approximation on Wikipedia and on other sites. If the ellipsoid is

x²/a² + y²/b² + y²/c² = 1

where a, b abd c are the equatorial radii then the surface area is approximately

4π(a^pb^p + a^pc^p + b^pc^p)^1/p

where p = 1.6075.

I hope this helps,
Harley