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If a cube is painted yellow on all faces and cut into 27 small cubes of equal size, then which of the following are correct?

A. Six cubes are painted on one face only.

B. There is only one cube which is not painted on any face.

C. There are six cubes which have two faces painted.

D. There are eight cubes which have three faces painted.

Solution

✅ Correct Option: 3

A cube with 27 small cubes will be equivalent to a rubik's cube (3×3×3)3\times3\times 3)

A. Six cubes are painted on one face only.

True, since the only central cube on each face will have one side painted.

6 faces →\rightarrow 6 cubes with one face painted only

B. There is only one cube which is not painted on any face.

True, it will a small cube located in the interior centre of the bigger cube.

C. There are six cubes which have two faces painted.

False, each edge will have a cube in the middle which will be painted exactly on two sides.

12 edges →\rightarrow 12 cubes with exactly two faces painted.

D. There are eight cubes which have three faces painted.

True The corner cubes of the bigger cube will have exactly three faces painted.

Hence, the correct option is Option 3.

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