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

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Question 67480: An open-top box is to be constructed from a 4 ft by 6 ft rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
Find the function V that represents the volume of the box in terms of x.

Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
The base of the new box, after the corners (x by x) have been removed, will have the dimensions (4-2x)ft. by (6-2x)ft. and the height of the box will be x ft.
The function, V, that represents the volume of the box will be:
V+=+%286-2x%29%284-2x%29%28x%29 Simplifying this:
V+=+%2824+-+20x+%2B+4x%5E2%29x or
V+=+4x%5E3+-+20x%5E2+%2B+24x