How many apples can I fit in a box using close packing of spheres?

[trillianK]

1. How many apples can you put into a box in the following dimensions:
Width: 1.25 meters
Length: 3 meters
height: 2.1 meters



2. Close packing of spheres



3. All I could find is the efficiency of close packing of spheres in face-centered cubic, which is 0.74048.

Is there an equation that takes into consideration the radius (I measured a few apples and it's about 3-4 cm) of the spheres (or the distance between the centers of two spheres, to be more precise) and the volume of the box to give the maximal number of spheres in the box?

Can I use all of that considering the fact that apples are not regular spheres? Am I thinking in the right direction?

I'm sorry if all of this sounds a bit silly, I come from a completely different walk of life and this is my only physics course.

Thanks for helping :)

 

[willem2]

I think calculating the volume of the box and using the maximum packing density for spheres of the same size will be enough. You could try how much apples fit in a smaller box, but I think you'd need hundreds of apples to get a reasonable estimate.

Of course with real world apples:
- you can fit in far more apples than you think.
- the apples at the bottom of the box will only be useful for applejuice.