Question: A rectangular box, whose edges are parallel to the coordinate axes, is inscribed in the ellipsoid 96x2 + 4y2 + 4z2 = 36. What is

A rectangular box, whose edges are parallel to the coordinate axes, is inscribed in the ellipsoid 96x2 + 4y2 + 4z2 = 36. What is the greatest possible volume for such a box?

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