# Math Help - green's theorem

1. ## green's theorem

How do i do this pls?
Find the volume of the greatest rectangular parallelopiped that can be inscribed in the ellipsoid:
x^2/a^2+y^2/b^2+z^2/c^2=1

2. Originally Posted by shushu
How do i do this pls?
Find the volume of the greatest rectangular parallelopiped that can be inscribed in the ellipsoid:
x^2/a^2+y^2/b^2+z^2/c^2=1
Are you allowed to assume that the largrest such parallelopiped has edges parallel to the axes? If so, then if a vertex in the first octant is (x,y,z) the eges have length 2x, 2y, and 2z. Maximize V= 8xyz subject to the constraint that $\frac{x^2}{a^2}+ \frac{y^2}{b^2}+ \frac{z^2}{c^2}= 1$.

Was there a reason for titling this "Green's theorem"? It doesn't seem to have anything to do with Green's theorem.