Question

If 3072cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Answer 1

I've tried to solve this twice now, and I end up with:\[\frac{ 147456 }{ 5\sqrt{5}}\] Can someone else take a crack at it and tell me if I'm right. I first write h in terms of x, as in \[h=\frac{ 3072- x^{2} }{ 4x} \] Then I write it in terms of Volume and derive it. Equal that to 0 to find the critical point within my range and substitute that in to get h again.
My Uni's webwork site tells me my answers wrong though.