Allied & ICAR Exam Bank • ALLIED_1663 MCQ • 1 Mark

Section 8: General Aptitude

Analytical & Spatial Aptitude

Subtopic: Spatial Reasoning & 3D Representations

Question Statement:

What is the theoretical maximum atomic packing factor (APF) for any arrangement of identical hard spheres in three-dimensional Euclidean space (Kepler conjecture)?

Options:

  • (A) pi / (3 * sqrt(2)) approx 0.7405 (74.05%)
  • (B) pi / 6 approx 0.5236 (52.36%)
  • (C) sqrt(3)*pi / 8 approx 0.6802 (68.02%)
  • (D) 1.00 (100%)

Answer Key:

A

Step-by-Step Solution & Explanation

The maximum sphere packing density in 3D is achieved by FCC and HCP lattices with packing fraction pi / (3*sqrt(2)) approx 74.05%.
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