Question Bank • QB_GA_094 NAT • 2 Marks

Section 8: General Aptitude

Analytical & Spatial Aptitude

Subtopic: Spatial Reasoning & 3D Representations

Question Statement:

A large solid wooden cube of side $6\text{ cm}$ is painted red on all six exterior faces and then cut into smaller identical cubes of side $1\text{ cm}$ each. Calculate the number of smaller cubes that have EXACTLY two faces painted red.

Answer Key:

48

Step-by-Step Solution & Explanation

For a cube of dimension $n = 6$ cut into unit cubes: - Cubes with exactly 2 faces painted lie along the 12 edges (excluding corners): $N_2 = 12 \times (n - 2) = 12 \times (6 - 2) = 12 \times 4 = 48$
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