# Re: max volume

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Posted by Soroban on September 26, 2002 at 02:34:45:

In Reply to: max volume posted by Kearney on September 26, 2002 at 02:15:54:

: I have a square cardboard, 15 by 15.
: I cut off a small square at each corner, then bend up the sides
: to form an open box.
: What is the maximum volume of such a box ?

Kearney, this is a standard problem in every Calculus book.
I don't say it's easy, just that it's very popular.

You have to sketch the problem.
You have a 15x15 square piece of cardboard.
You cut out smaller x-by-x squares at each corner.
(I'll try to type the diagram.)
_ _____ _
|_| |_| x
| |
| |15-2x
|_ _|
|_|_____|_| x
x 15-2x x

The four flaps are folded up to form a box. Can you picture the
length, width, and height of the box?

The length and width are the same. They will be 15-2x.
The height of the box is x. (Do you see why?)

So, the Volume (LxWxH) = x(15-2x)^2

Now, you can maximize this function.

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