Thread: Find the volume of the largest rectangular box with edges parallel to the axes that c

Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid

Hint: By symmetry, you can restrict your attention to the first octant (where ), and assume your volume has the form . Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:

Originally Posted by ewkimchi

Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid

Hint: By symmetry, you can restrict your attention to the first octant (where ), and assume your volume has the form . Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant. Maximum volume:

Maximise V subject to the given constraint (the equation of the ellipsoid). Please show your work and say where you get stuck if you need more help.