Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid x225+y216+z281=1 x225+y216+z281=1 Hint: By symmetry, you can restrict your attention to the first octant (where x, y,z≥0x, y,z≥0), and assume your volume has the form V=8xyzV=8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume: