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
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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