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GO Classes | IIITH PGEE 2026 Mock Test 12 | Question: 40

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The large cube shown is made up of $27$ identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is

  1. $10$
  2. $16$
  3. $20$
  4. $22$

1 Answer

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Clearly, no unit cube has more than one face painted, so the number of unit cubes with at least one face painted is equal to the number of painted unit squares.

There are 10 painted unit squares on the half of the cube shown, so there are $10 \cdot 2=20$ unit cubes with at least one face painted, thus our answer is C .
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