A box with an open top will be constructed from a rectangular piece of cardboard. The piece of cardboard is 10 inches wide and 14 inches long. The box will be

Question

constructed by cutting out equal square of side x at each corner and then folding up the sides. What is the appropriate domain for the function V(x) that gives the volume of the box as a function of x?

Answer 1

Let x = length of a side of a square

 

The base of the box is a rectangle with dimensions 10 - 2x by 14 - 2x.  The height of the box is x.  

 

Volume = V(x) = x(10-2x)(14-2x)

 

Since x is the height of the box, x must be positive.

 

Also, the dimensions of the base of the box must be positive, so x < 5.

 

Domain:  0 < x < 5