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smithcherry smithcherry
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11 years ago
There is a box that has dimensions of 30 by 20 but you have to fold the corners of the box up which is replaced by the variable x. how would i find the maximum volume of the box by cutting the corners.
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#1
11 years ago
Do you mean that you are starting with a rectangle of thin material 30 by 20? You then cut small squares of side x from each of the four corners. Then you fold up the sides?

The final box will have dimensions 30 - 2x, 20 - 2x, x so its volume
V = x(30 - 2x)(20 - 2x)
Multiply out and find dV/dx. Solve dV/dx = 0 to find the value of x that maximises volume.
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