Math 125-103
Fall 2012
Quiz 2
A box with an open top is to be constructed from a rectangular
piece of cardboard that is 14 inches by 22 inches by cutting out
equal squares of side length x from each corner and folding up the
sides as indicated. Express the volume as a function of x.
x
Carter
x
x
x
x
14”
x
22”
Solution. The edge lengths of the open box are x, 14 − 2x, and
22 − 2x. Therefore the volume is
V = x(14 − 2x)(22 − 2x).
For the purposes of future problems, it is not wise to multiply out the
solution.
V = 4x3 − 72x2 − 308x.
1
x
x