1. The problem statement, all variables and given/known data Find the volume of the largest rectangular box with faces parallel to the coordinate planes that can be inscribed inside the ellipsoid : (x^2/a^2)+(y^2/b^2)+(z^2/c^2) = 1 2. Relevant equations Volume of a rectangular box = x * y * z critical point formula. 3. The attempt at a solution The volume of a box is maximised when x = y = z ?