# Thread: box with a lid

1. ## box with a lid

Hello
I need to construct a box with a seamless flap lid that extends down the front to the bottom, (sorta like a pizza box) from a single piece of paper 18x20 that maximizes volume. I solved the open box max volume problem but having a lot of trouble with this one. Can anyone help or show me where to look? Thank you!

I'm not quite sure what you are asking?

It is just a rectangular prism of any dimensions, as long as the surface area = 18x20?
I am not sure if there are any parts of the box that overlap.

EDIT: Squares/Cubes are are always better for maximizing area/volume. So if there are no restricions on the boxes dimensions it would be a cube. If the height is restricted (so it is short like a pizza box) then it would have that height, with a square base.

Ok we are given a sheet of paper 18x20. From that I need to design a box maximixing the volume which is very similair to a pizza box. The clam shell bottom piece has a bottom and three sides, the top has the same 3sides and a top, and finally they are connected using another side forming the back side. So this box overall will have 9 surfaces because the top and bottom fold clam shell over one another. THanks so much!

4. Hello, jkupcha!

I have another question . . .

I need to construct a box with a seamless flap lid that extends down the front to the bottom,
(sort of like a pizza box) from a single piece of paper 18×20 that maximizes volume.

Can the seven panels be cut separately from the 18×20 paper?

Or does the box need to be folded from a single (strangely shaped) piece?

(I don't know what "seamless flap" means in this context.)

5. Hello, jkupcha!

I don't agree with your description . . .

We are given a sheet of paper 18x20.
From that I need to design a box maximixing the volume which is very similair to a pizza box.
The clamshell bottom piece has a bottom and three sides,
the top has the same 3 sides and a top, . ... I don't agree
and finally they are connected using another side forming the back side.
So this box overall will have 9 surfaces because the top and bottom fold
clam-shell over one another.
Are you sure of that?
Can you give us the wording of the original problem . . . or a diagram?

From your original post, I assumed the box looked like this:

Code:
            *-------*
/       / \
/       /   \
/       /     \
*-------*       \
\       \
*-------\       \
/|        \     /|
/ |         \   / |
/  |          \ /  |
*---------------*   *
|               |  /
|               | /
|               |/
*---------------*