posted by Z32 .
If 6075 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Volume=??? cubic cm
Use the same procedure explained in previous problems of this type, and show your work.
You have two variables, box base length a and height h. I will assume cutout corner square pieces are not used; other wiseyou will need a lot of tape to make sides from cut corners.
(a + 2h)^2 = 6075
The box will be made by folding up the four protruding ends of a fat looking cross, made by cutting square corners off a square that has side length a + 2h.
Volume = a^2*h
Express volume V in terms of a or h only and set the derivative with respect to the remaining variable equal to zero.
Compute the two variables and the volume