Question

Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid x^2/81+y^2/25+z^2/49=1

Answer 1

This site discusses the problem, as well as a trick shortcut:

http://math.stackexchange.com/questions/129249/maximize-volume-of-box-in-ellipsoid

google will provide other solutions as well.