Pepe Chapuzas asked...
If the eccentricity of an ellipse is e , what is the ratio between the volumes of both spheroids?
And Nina Guindilla answered...
Let a and b be the major semiaxis and the minor semiaxis of the ellipse.
Let v and V be the volumes of the oblong spheroid and that of the oblate one.
v = 4πab2/3
V = 4πa2b/3
v / V = b / a = √ (1−e2)