GATE EE 2025 Set 1 — Question 9
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
Spheres of unit diameter are centered at where , and take every possible integer values.The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, is the distance to its nearest sphere and is the distance to its next nearest sphere. The value of is:
Correct answer
(C) √(2)
Solution
The centers of the spheres form a simple cubic lattice with a lattice constant (since the centers are at integer coordinates).Consider a sphere centered at the origin :
1.The nearest spheres are located at , , and . The distance to these spheres is .
2.The next nearest spheres are located at , , and . The distance to these spheres is .
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