Small-sphere statistics

Volume calculation

Provided next are small-sphere statistics based on spheres whose diameter ranges from 2.0 mm down to 0.063 mm. The volume (V) is calculated using the formula V = 4/3 x ∏ x r³ (r = radius).

Quantity and number of contact points

Sphere

Mini-sphere: V = 4/3 x π x 0,0315 x 0,0315 x 0,0315 = 0,0001309 mm³

Maxi-sphere: V = 4/3 x π x 1 x 1 x 1 = 4,188 mm³

Mathematically, 31,993 mini spheres therefore have the same volume as a maxi sphere 2.0 mm in diameter. If the spaces between the mini spheres are also taken into account, about 20,000 such spheres would still fit into a maxi sphere.

In a cube with a side of 10 cm, the densest packing can be achieved by surrounding a sphere with 12 others in each case. A few trigonometric functions and Pythagoras' theorem can then be used to calculate the corresponding, maximum number of spheres the cube can hold.

The table below provides rounded values for different sphere diameters.

Diameter (in mm) Number (rounded) Contact points (total) Pore width in (µm)
0,063 5,6 billion 67 billion 9,8
0,125 720 million 8,5 billion 19,3
0,25 90 million 1 billion 38,7
0,5 11,2 million 134 billion 77,4
1,0 1,4 million 16 million 155.0
2,0 172.000 2 million 310.0