Math CentralQuandaries & Queries


Question from Le, a student:

Metal Fabrication; If an open box is made from a tin sheet 8 in square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. (???) confused

Hi Le,

Here is the picture I see.


A 8 inch square sheet of tin (brown) has equal sized squares (yellow) cut our from each corner. I let these squares be x inches by x inches. (How long is s in terms of x?) The sides are folded up along the black lines to form a box.


What are the dimensions of the box? What is the volume of the box? Use the calculus you know to maximize the volume.

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