Question

The total volume of rhombohedron with face angle 60° is _______

(a) 0.5

(b) 0.7071

(c) 0.9099

(d) 1

This question was addressed to me during an interview for a job.

My question comes from Packing of Uniform Spheres in portion Preliminary Definitions and Relationships of Geotechnical Engineering I

Answer 1

Correct answer is (b) 0.7071

The explanation is: The total volume of rhombohedron is given by,

V = (1-cosα)*(√(1+2cosα))

V = (1-cos60°)*(√(1+2 cos60°))

V = 0.7071.