I am trying to make a box 18" wide x18" tall. With in this box I need 12 smaller boxes.?

Question

Is there any formula to figure out what size the boxes inside will be?

Answer 1

this is a simple thinking problem let' assume that you are talking about a cubic box so the depth is also 18 inches.
if you want 12 boxes, think of 2 layers fo 6 boxes
so each layer of boxes will be 9 inches tall.
They will be 9 inches deep and 6 inches wide.
If you want a formula, it would be The original box volume of 18 x 18 x 18 = 5832
divide by 12 = 486
Dimension of each of 12 box will be lwh = 486
Where l w and h each must be < 18

Answer 2

It depends what shape you want the inside boxes to be. You have 18^3, or 5,832 cubic inches. You need 12 smaller boxes. We could arrange them in two rows, with 6 in each row. Each row could be 3 boxes wide and 2 boxes high. Then the outside of each box would be 6" long, 9 inches wide, and 9 inches tall.
Or, we could make 12 boxes, 18" x 18" x 1 1/2", that stack on top of each other.

We have 5832 cubic inches to work with. If we make all the boxes the same volume, each will be 5832/ 12 = 486 cubic inches.

If we want each of the 12 boxes to be a cube, then we need the length , width, and height of each box to the the cube root of 486, or 486 ^(1/3) = 7.86 inches (approximately).

The problem with this is, the nice 7.86-inch cubes won't stack into the 18" big box because 7.86 does not go into 18 evenly!!!!!

I think you'll just need to experiment with how you want the 12 boxes arranged inside the big box and play with it some.

Another thing you may want to consider, do you need all the boxes accessible from the top of the big box, or a side of the big box, or does it matter?

Interesting question.

Answer 3

Do you want them all the same size?

18"x18" interior provides for 18x18=324 sq inches of area.

324/12 = 27, or the area of 12 identical sized boxes.

Boxes 3"x9" would give you 27 sq inch boxes.

So, 12, 3"x9" boxes would fit within 18"x18".

Since you are talking about a box, you likely mean a three dimensional box which includes depth, with three measurements, say 18"x18"x18".

18x18x18 = 5832, total interior volume
5832/12 = 486, total volume for each of 12 interior boxes
So 12 of any box with volume of 486 would fit.

Many measurements would produce this volume:

9x9x6
18x9x3
27x9x2
54x3x3

Answer 4

Your volume is 5832 cubic inches. Divide this by 12 and get 486 cubic inches for each box. Take the cube root of that and get 7.862224183 inches per side assuming you want cube boxes.