Volumes of the maximum inscribed box of an elipsoid

Description

An ellipsoid is a closed quadric surface that is a three dimensional analogue of an ellipse.a, b, c.are called the semi-principal axes.They correspond to the semi-major axis and semi-minor axis of the appropriate ellipses.
There are four distinct cases of which one is degenerate: a>b>c — tri-axial or (rarely) scalene ellipsoid; a=b>c — oblate ellipsoid of revolution (oblate spheroid); a=b<c — prolate ellipsoid of revolution (prolate spheroid); a=b=c — the degenerate case of a sphere;
The volume of the maximum inscribed box of an elipsoid can be calculated by the semi-principal axes a,b,c of the elipsoid.