Question 87115
From a 12cm by 12cm piece of cardboard, square corners are cut out so that the sides can be folded up to make a box. Express the volume of the box as a function of the length, x, in centimeters, of a cut-out- square and determine a reasonable domain for this function. 
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Let an edge of the cutout square be x.
After sides are folded up the bottom of box is a 12-2x by 12-2x square.
The height of the box is x.
Volume = length*width*height
Volume = (12-2x)(12-2x)x
Volume = 4x(6-x)^2
Volume = 4x[36-12x+x^2)
Volume = 4x^3-48x+144x
Domain: Since the base is 12-2x by 12-2x a reasonable domain would be 0 < x < 12
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Cheers,
Stan H.