maximum volume box project help

[casey123]

Hi, My Pre-Calc class is doing the "box project" I was able to finish all 3 of the problems except the extra-credit one. Can anyone help me with the formula for this problem? I just don't seem to get this particular one? thanks so much ........ With a piece of paper that is 21 by 18 in. I need to build a mailing box that gives the maximum volume.

 

[galactus]

When a box is built from a sheet of cardboard or paper, squares are cut from each corner.

Start by cutting squares of side length x from each corner.

Then, when you bend up the sides, you have a box.

Try picturing it. Draw a diagram. The size of the squares determines the box's depth.

 

[casey123]

thanks... I solved the open box problem but this has to be a closed box with flaps like those used for mailing.

 

[mmm4444bot]

See THIS THREAD for a diagram of a box with lid. (You should probably add another flap along the distal end of the lid, so that the end of the lid folds over onto the side of the box for sealing.)