Asquare piece of tin has 12 inches on a side. an open box is formed by cutting out equal square pieces at the corners and bending upward the projecting portion which remain. find the maximum volume that can be obtained.

Explanation:

Given a square Piece whose side is 12 inches

Now square pieces are cut from each corner to make it a open box

Suppose x is the length of square piece at each corner

then

base square has a length of

Dimension of new box is

Volume

For maximum volume differentiate with respect to x we get

we get x=6 and 4 but at x=6 volume becomes zero therefore x=4 is valid

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