Posted by **jim** on Tuesday, May 19, 2009 at 8:05pm.

You are planning to make an open-top box from an 12 in by 12 in piece of cardboard

by cutting congruent squares from the corners and folding up the sides.

What are the dimensions (of the 3 sides) of the largest volume you can make this way?

- calculus -
**Reiny**, Tuesday, May 19, 2009 at 8:19pm
let the size of the cut out squares be x by x inches

so the base of the box is 12-2x by 12-2x and its height is x inches.

volume = x(12-2x^2

expand, then find d(volume)dx

set that equal to zero and solve for x,

from which you can then find the dimensions

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