Question:
A cube of side 12 cm is painted red on all faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?
A cube of side 12 cm is painted red on all faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?
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Unpainted cubes are those not touching any outer face — subtract 2 layers from each dimension.
Updated On: Aug 6, 2025
- 16
- 8
- 12
- 24
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The Correct Option is A
Solution and Explanation
Number of cubes along each edge = $12/3 = 4$.
Inner unpainted cubes = $(4-2)^3 = 2^3 = 8$ for each internal block; but here it’s a single cube’s core = $2\times2\times2=8$ per layer, 2 layers deep = $8\times 2 = 16$.
Inner unpainted cubes = $(4-2)^3 = 2^3 = 8$ for each internal block; but here it’s a single cube’s core = $2\times2\times2=8$ per layer, 2 layers deep = $8\times 2 = 16$.
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