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.
A. 1:4 B. 1:3 C. 1:2 D. 2:3
GATE 2015 · General Aptitude · Ratio Proportion · medium
Answer: Visible : Non-visible = 1 : 2 (Answer C)
Total faces of all small cubes: 27 small cubes, each with 6 faces: 27 x 6 = 162 total faces
Count visible (outer surface) faces: The big cube has 6 faces. Each face is a 3x3 grid of small cube faces. So 6 x 9 = 54 visible faces.
Count non-visible faces: 162 - 54 = 108 faces are hidden inside the structure.
Compute the required ratio: Divide both by 54: 54/54 : 108/54 = 1 : 2