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GATE 2015 EC – Question 9

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.

  1. 1 : 4
  2. 1 : 3
  3. 1 : 2
  4. 2 : 3

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Show answer and explanation

Correct answer: (C) 1 : 2

Explanation

There are $3^3 = 27$ small cubes with $27 \times 6 = 162$ faces in total. The visible faces are the outer faces of the big cube, which is $6 \times 9 = 54$. The faces not visible number $162 - 54 = 108$. The ratio is $54 : 108 = 1 : 2$.