About the surface area of a prolate ellipsoid

[Tahmeed]

Main Question or Discussion Point

Is there any limit for which we can approximately write the surface area of a prolate ellipsoid to be 4piA*B comparing with the spherical 4piR*R??

 

[haruspex]

Is there any limit for which we can approximately write the surface area of a prolate ellipsoid to be 4piA*B comparing with the spherical 4piR*R??

Look at eqn 9 at http://mathworld.wolfram.com/ProlateSpheroid.html.
You could substitute for a in terms of c and e using eqn 8, then make an approximation for small e.

 

[Tahmeed]

Look at eqn 9 at http://mathworld.wolfram.com/ProlateSpheroid.html.
You could substitute for a in terms of c and e using eqn 8, then make an approximation for small e.

I don't know why but the link isnt working for me. However does it bring 4piAC as a result?

 

[haruspex]

I don't know why but the link isnt working for me. However does it bring 4piAC as a result?

It can't be exactly that, of course, so it depends how good an approximation you want.
The exact equations at that link are
Area = $2\pi a^2+2\pi ac\sin^{-1}(e)/e$, eqn (9), and $a^2=c^2(1-e^2)$, eqn 8
where the radii are a, a, c.