If 1900 square centimeters of material is available to make a box with a square base and an open top

Question

find the volume !

Answer 1

avgjoe is correct as long as the box is a "cube." take into account that just because a box has a square base does not mean it is a cube. it could be a square prism, and the lateral faces could be rectangles. if the box is a cube, then avgjoe did it correctly.

Answer 2

1900/5=380

sqrt 380=19.49

19.49^3=7403.47

Answer 3

This is an elementary calculus problem.  We want V = h b^2, where b^2 + 4bh = A, the given area (1900 in this case).  Solve the latter for h to get h = (A-b^2)/4b, substitute this in the first equation to get V = (A-b^2)/4b b^2, and simplify to get V = b(A-b^2)/4 = (Ab - b^3)/4.  Take the derivative with respect to b to get dV/db = A/4 - 3b^2/4.  Equate to zero to get A = 3b^2.  Plug in the given value for A, compute b, compute h, and you're done.