As shown in the figure below, an open box is to be constructed from a rectangular sheet
of metal, 10 in by 18 in, by cutting out squares with sides of length x from each corner and
bending up the sides. What length x should we cut to create a box with the largest possiblevolume? Recall that the volume of a rectangular box is the product of it length, width, and
height.

Question

As shown in the figure below, an open box is to be constructed from a rectangular sheet
of metal, 10 in by 18 in, by cutting out squares with sides of length x from each corner and
bending up the sides. What length x should we cut to create a box with the largest possiblevolume? Recall that the volume of a rectangular box is the product of it length, width, and
height.

campbell_st · Answer

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the dimensions are     length  18 - 2x
                                 width   10 - 2x
                                  Height  x 

so the volume is V = x(18-2x)(10-2x)

                         V = 4x^3 -56x^2 + 180x

you are looking to find the 1st derivative and solve for x