a solid cube of 12 cm has been painted green in two adjacent sides, yellow in other two adjacent sides and blue in two opposite sides. it is then cut into cubical blocks of side 4 cm each.how many cubes have no face painted?

A 12 cm cube cut into 4 cm cubes yields exactly 3 cubes along each edge, for a total of 3×3×3=273\times 3\times 3=273×3×3=27 small cubes.

The unpainted cubes (no faces painted) are those completely inside, away from all outer surfaces: form a smaller 1×1×1 cube at the core, since you remove 1 layer from each side (3−2=13-2=13−2=1 per dimension). Thus, 1 cube has no paint.

Why the Painting Doesn't Affect This

The green (adjacent faces), yellow (other adjacent), and blue (opposite faces) only color the outer surfaces —internal faces exposed by cuts stay unpainted. Unpainted small cubes have all faces originally internal , so the answer holds regardless of colors.

Quick Visualization

• Outer layer : All 26 surface small cubes touch at least one painted face.
• Core : Only the single middle cube in the 3×3×3 grid avoids all paint.

TL;DR : Exactly 1 small cube has no face painted.