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.
Options:
(A) 1 : 4
(B) 1 : 3
(C) 1 : 2
(D) 2 : 3
Official Answer Key:
C
Step-by-Step Solution & Explanation
Total small cubes = 3³ = 27, and each has 6 faces, so total faces (visible + hidden) = 27×6 = 162.
Visible faces = total exterior surface area of the assembled 3×3×3 cube, expressed in unit-square faces = 6 × (3×3) = 54.
Hidden (not visible) faces = 162 − 54 = 108.
Ratio visible : not visible = 54 : 108 = 1 : 2. Hence (C) is correct.
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