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The volume if voids of a rhombohedral array of spherical grains with α=75° is _______

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in Geotechnical Engineering I by (102k points)
The volume if voids of a rhombohedral array of spherical grains with α=75° is _______

(a) 0.4266

(b) 0.7439

(c) 0.3895

(d) 0.3595

I had been asked this question by my school teacher while I was bunking the class.

Question is from Packing of Uniform Spheres topic in chapter Preliminary Definitions and Relationships of Geotechnical Engineering I

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Best answer
Right choice is (c) 0.3895

Easiest explanation: Given,

α=75°

The total volume V=(1-cosα)*(√(1+2cosα))

∴ V=(1-cos75°)*(√(1+2cos75°))

V=0.9131

Volume of the solids Vs=(π/6)=0.5236

Volume of the voids Vv=V-Vs=0.9131-0.5236

Vv=0.3895.

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