Question

an 18 inch by 20 inch sheet of cardboard is cut and folded to make a box for the great pecan company.
a. write a polynomial funtion to model the volume of the box.

how can i graph this?

c. the company wants the box to have a volume of 224 cubic inches. write an equation to model this situation.
d. find a positibe integer for x.

Answer 1

I will asssume that you are going to cut equal squares from each of the four corners to do this.
Let each side of a square be x inches.

then the length of the box will be 20-2x
its width will be 18-2x in
and its height will be x in

since Vol = length x width x height

Vol = x(20-2x)(18-2x)

make a table of values, noting there are zeros at x=0, x=10 and x=9

b) x(20-2x)(18-2x) = 224

c) expanding this and simplifying I got

x^3 - 19x^2 + 90x - 56=0

I ran this through the following cubic equation solver

http://www.1728.com/cubic.htm

and got x=6.529, the other two answers are extraneous.

(check my work, I tend to get careless at this time of night)