SOLUTION: An 18-inch by 20-inch sheet of cardboard is cut and folded to make a box for a comany. Write a polynomial function to model the volume of the box.

Question 229322: An 18-inch by 20-inch sheet of cardboard is cut and folded to make a box for a comany. Write a polynomial function to model the volume of the box.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An 18-inch by 20-inch sheet of cardboard is cut and folded to make a box for a comany. Write a polynomial function to model the volume of the box.
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V(x) = (18-2x)(3-2x)x
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Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The polynomial function model for the volume of a box made from a sheet of something depends a great deal on exactly what sort of box you intend to make. Typically in this sort of problem, it is an open-topped box formed by cutting squares out of the corners of the sheet of material and folding up the sides. If that is an incorrect assumption for this problem, tough -- you should have been more specific.

Let represent the measure of the side of one of the squares cut out of each corner. Then the length of the resulting box will be , the width of the resulting box will be , and the height of the resulting box will be simply . The volume of a box is length times width times height, so:

All you need to do is multiply it out and collect like terms.

John

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