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A cube is coloured red on two opposite faces, blue on two adjacent faces and yellow on the two remaining faces. It is then cut into two halves along the plane parallel to the red faces. One piece is then cut into four equal cubes and the other one into 32 equal cubes
Let's take the original side length of the cube to be 2a
Cutting the square parallel to the red faces, would give us:
Let's say we cut the upper piece into four equal squares.
The upper piece is a cuboid with dimensions (2a, 2a, a)
To make four cubes we can cut it into equal halves along is height and length.
To cut the lower piece into 32 equal pieces, we can put 3 cuts along its length, 3 cuts along its height and breadth
We want to see how many of these 36 cubes will not have any red faces.
All the four pieces from the upper half of the original cube will have one red face.
From the lower piece, of the 32 pieces, only the bottom 8 would have a red face, the other 24 would not have any red faces.
Therefore, Option D is the correct answer.
