How do I calculate the packing efficiency of hexagonal closest packing structure?
How do i calculate the efficiency of packing (spheres)
Hexagonal closest packing:
bottom layer: 3 spheres
middle layer: 7 spheres
top layer: 3 spheres
any help would be greatly appreciated 
1) Hexagonal closest packing (efficiency = 74%)
2) Cubic closest packing - (efficiency = 74%)
3) Body-centered - (efficiency = 68%)
I know the efficiency values because they are in my textbook and all over the internet.
efficiency = Volume of the spheres/Volume of a box around the spheres.
the spheres in my model have a radius of 3cm, so volume of the spheres is easy... 4/3(pie)r^3 x (number of spheres)
Hexagonal closest packing: 13 balls in total in 3 layers.
bottom layer: 3 spheres
middle layer: 7 spheres
top layer 3 spheres
Cubic closest packing : 13 balls in total in 3 layers
bottom layer: 4 balls
middle layer: 5 balls
top layer: 4 balls
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