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Tahmeed
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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??
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Look at eqn 9 at http://mathworld.wolfram.com/ProlateSpheroid.html.Tahmeed said: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??
I don't know why but the link isn't working for me. However does it bring 4piAC as a result?haruspex said: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.
It can't be exactly that, of course, so it depends how good an approximation you want.Tahmeed said:I don't know why but the link isn't working for me. However does it bring 4piAC as a result?
A prolate ellipsoid is a three-dimensional shape that is similar to an elongated sphere. It is created by rotating an ellipse around its major axis.
The surface area of a prolate ellipsoid can be calculated using the formula 4πab, where a is the semi-major axis and b is the semi-minor axis. This formula assumes that the prolate ellipsoid is symmetrical along its major axis.
A prolate ellipsoid is elongated along its major axis, while an oblate ellipsoid is flattened along its major axis. This means that the semi-major axis is longer than the semi-minor axis in a prolate ellipsoid, while the opposite is true for an oblate ellipsoid.
As the major axis of a prolate ellipsoid increases, the surface area also increases. However, the surface area decreases as the minor axis decreases. This is because a longer major axis results in a more elongated shape, while a shorter minor axis results in a more compact shape.
Prolate ellipsoids are commonly used in engineering and physics, particularly in the design of spacecraft and satellites. They are also used in biology to model the shape of cells and protein molecules.