We want to make a box using a piece of cardboard that is 12 inches along each side. To form the box, we cut squares at each corner and then fold up the sides. What will be the dimensions (l x w x h) of the box with the maximum volume?

Question

We want to make a box using a piece of cardboard that is 12 inches along each side.  To form the box, we cut squares at each corner and then fold up the sides. What will be the dimensions (l x w x h) of the box with the maximum volume?

miracrown · Answer

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I've made a sketch of the original piece of cardboard measuring 12 in on each side.
and have drawn the corner cutouts.