i Need to calculate volume of parallelopiped of maximum volume with edges parallel to the coordinate axes that can be incribed in a ellipseoid $(x/a)^{2} + (y/b)^{2} + (z/c)^{2} =1$ .
Apparently there is no problem in solving question .BUT I TOOK volume V=xyz with x,y,z are dimensions of rectangular parallelopiped .
Doubt : In textbook they have taken V=8xyz with dimensions $2x,2y,2z$ while i have taken $x,y,z$ . So i am getting coordinated with each coordinate divided by 1\2 than that of answer . I want to know why they have taken dimensions like this and maximize $8xyz$ instead of $xyz$ ..