Optimization: Square box

[peblez]

A box is to be made from a square piece of cardboard that measures 12 cm x 12cm, by having equal squares cut from the corners and turning them up to form the sides. Find the dimensions of the box of greatest volume that can be made this way.

Can some one explain or draw a diagram depicting this question. I can not find the formula needed to maximize this problem. thanks

 

[skeeter]

sketch a picture ... let x = side length of the square that is cut out from each corner.

when it is folded up, the box will have the following dimensions

length = 12 - 2x
width = 12 - 2x
height = x

V = LWH