Pre Calc Open Box Problem?
An open box is formed by cutting squares out of a piece of cardboard that is 18 ft by 13 ft and folding up the flaps.
what size corner squares should be cut to yield a box that has a volume of 155 cubic feet?
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Verified answer
Let x = dimension of square corner cut-outs.
Then the volume is:
V = (13 - 2x)(18 - 2x)x
= (234 - 62x + 4x^2)x
= 4x^3 - 62x^2 + 234x
Set this equal to 115:
4x^3 - 62x^2 + 234x = 115
4x^3 - 62x^2 + 234x - 115 = 0
Unfortunately, this does not factor. To get the answer, I used an online cubic equation solver. Here are the 3 possible answers:
9.86579948756889 <-throw this one out because it is too big
0.57613029167498 <----this is a solution
5.05807022075613 <----this is a solution