how do I caluclate how many little boxes go into a volume of 6650 cubic inches?

Question

I've got demensions of a product that we put in bigger boxes to pick from. I'm wondering what would be the best way to calculate how many little boxes I could fit in 65% of the 6650 cubic inches. Taken that we have XYZ as the demensions for every individual "inner package" how would I calculate how many of XYZ pachages I could fit into 65% of 6650 cubic inches? Please help

For instance here is a product we have:
The demensions for this small pack that is to go into the big box is : 5x3.2x13.00 wich gives us a volume of 21.20 cubic inches right? do I just divide that number in 65% of 6650 cubic inches which is 4322.50? to get the amount of small packages i can fit in that 65% portion of the box?

Answer 1

The relative dimensions are important here. If the little boxes are the smallest possible cubes and the big box is a cube, you will optimize packing. You do not give enough detail to solve the problem.

From addiitonal details: There is still not enough info. The dimensions of the big box are also critical. Consider that a 6650 cubic inch box could have dimensions 1"x1"x6650", in which case zero of your small boxes would fit.

Answer 2

First you must calculate the volume of the little box and then find 65% of 6650 and then divide this answer by the volume of little box.

Answer 3

A rough estimate would be (.65 x (volume of large box))/(volume of small box). However, this may not be accurate. You need to consider how the dimensions relate to each other. If the dimensions of your small box divide the dimensions of your large box, you're fine. If not, you'll have to experiment with how to best arrange the boxes. It can be a difficult problem.