GATE_AE_2027_MOCK_01_Q10 GATE 2027 Aerospace Engineering All-India Master Mock 01 (Foundation & Standard Core Calibration) NAT · 2 Marks
General Aptitude • Analytical & Spatial Aptitude • Spatial Reasoning & Paper Folding

A solid rectangular avionics chassis of dimensions $12\text{ cm} \times 8\text{ cm} \times 5\text{ cm}$ has all its exterior faces painted with an anti-static coating. The chassis is then cut completely into unit cubes of $1\text{ cm} \times 1\text{ cm} \times 1\text{ cm}$. How many of these unit cubes have anti-static paint on EXACTLY TWO faces?

Answer Key:
76

Step-by-Step Verified Solution

### Solution: Cubes with paint on exactly 2 faces lie along the 12 edges, excluding the 8 corners: $4 \times (12 - 2) + 4 \times (8 - 2) + 4 \times (5 - 2) = 4(10) + 4(6) + 4(3) = 40 + 24 + 12 = 76$. Correct: 76.
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