Precalc
posted by Julie .
A cardboard box with an open top and a square bottom is to have a volume of 45 ft3 . Use a table utility to determine the dimensions of the box to the nearest 0.1 foot that will minimize the amount of cardboard used to construct the box.

Let the side of the bottom square be x, and the height of the box, h.
The volume is x²h=45
or
h=45/x²
The total surface area (5 faces) is
S=x²+4(x*h)=x(x+4h)
Make a table of 3 columns, comprising x, h and S. The value of x could vary between 4 and 5 in 0.1 ft intervals.