Posted by **Julie** on Sunday, September 26, 2010 at 3:54pm.

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.

- Pre-calc -
**MathMate**, Sunday, September 26, 2010 at 5:30pm
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.

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