Discussion
Ramesh has a metal cube. He paints all sides of the cube with green color. He divides the cube into smaller cubes of volume 1 cu.m. each. How many of these smaller cubes will not have green color on even one of its sides if the volume of larger cube is 27 cu.m.?
Answer: B
A cube of volume 27 m³ has edge \( \sqrt[3]{27} = 3 \) m, so it cuts into \( 3 \times 3 \times 3 \) unit cubes.
Only the cubes strictly inside - not touching any face - escape the paint. Removing one layer from each of the six faces leaves a cube of side
\[ 3 - 2 = 1 \]
\[ \text{unpainted cubes} = 1^{3} = 1 \]
The general result for an \( n \times n \times n \) cube is \( (n-2)^{3} \), which is why a 3-cube yields just the single central cube.
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