Question Bank • QB_GA_ASA_008 NAT • 2 Marks

Section 8: General Aptitude

Analytical & Spatial Aptitude

Subtopic: Spatial Reasoning & 3D Representations

Question Statement:

For the same $4\text{ cm}$ solid cube painted green on all faces and cut into 64 unit cubes of $1\text{ cm}$, the total number of smaller cubes having AT LEAST one face painted green is ________ (answer in integer).

Answer Key:

56

Step-by-Step Solution & Explanation

1. Total number of unit cubes $= 64$. 2. The only cubes with zero painted faces are those located entirely within the inner core of dimension $(n - 2) \times (n - 2) \times (n - 2)$: $N_{\text{0-face}} = (4 - 2)^3 = 2^3 = 8$ 3. Cubes with at least one face painted: $N_{\ge 1} = \text{Total} - N_{\text{0-face}} = 64 - 8 = 56$
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