SOLUTION: An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of

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Question 29189: An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
I need to find the function V that represents the vloume of the box in terms of x
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the length of the side of the square to be cut from each corner of the original 4 X 6 piece of cardboard.
The dimensions of the base of the newly-formed box will be: (4 - 2x) X (6 - 2x) and, of course, the height will be x. Now you can write the function for the volume, V, of the newly-formed box, based on the formula for the volume of a rectangular prism (box): V = L*W*h
V+=+%284-2x%29%286-2x%29x Simplify.
V+=+%2824-20x%2B4x%5E2%29x
V+=+24x-20x%5E2%2B4x%5E3 Rewrite as:
V+=+4x%5E3-20x%5E2%2B24x