A cube of side 125 cm is painted red on all the faces and then cut into smaller cubes of sides 25 cm...........

Logical Resoning (CGL) Cubes and Dice

A cube of side 125 cm is painted red on all the faces and then cut into smaller cubes of sides 25 cm each. Find the number of

smaller cubes having at least two faces painted.

This questions was previously asked in

SSC CGL 12th April 2022 Shift-3

- The original cube has a side of 125 cm and is cut into smaller cubes with 25 cm sides.

- The resulting smaller cubes will be 5x5x5 in quantity because \(125 \div 25 = 5\).

- Each face of the large cube has \(5 \times 5 = 25\) small cubes.

- Edge cubes are shared between two adjacent faces and each edge contains \(5 - 2 = 3\) cubes excluding the corners.

- With 12 edges, the total edge cubes having two painted faces amount to \(12 \times 3 = 36\).

- Each corner cube, shared among three faces, sums up to \(8\) cubes.

- Altogether, the number of cubes with at least two painted faces is \(36 \text{ (edges) } + 8 \text{ (corners) } = 44\).

Option 3: 44 is correct.

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