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A cube of volume 64 cm3 is is cut into two smaller and identical cuboids. The faces of dimensions 4 × 4 of one of the cuboids are painted with black color and the rest of its faces are painted with yellow color. One pair of adjacent faces that do not include any face of dimensions 4 × 4 of the other cuboid are painted with yellow color and the rest of its faces are painted with black color. Now each of two cuboids are cut into 32 smaller and identical cubes. How many of the smaller cubes have exactly three colored faces?

A cube of volume 64 cm3 is is cut into two smaller and identical cuboids. The faces of dimensions 4 × 4 of one of the cuboids are painted with black color and the rest of its faces are painted with yellow color. One pair of adjacent faces that do not include any face of dimensions 4 × 4 of the other cuboid are painted with yellow color and the rest of its faces are painted with black color. Now each of two cuboids are cut into 32 smaller and identical cubes. How many of the smaller cubes have exactly three colored faces? Correct Answer 8

Let the each side of original cube be 12 units.

According to the question, the cube of volume 64 cm3 is is cut into two smaller and identical cuboids and each of two cuboids are cut into 32 smaller and identical cubes.

Therefore, the number of cubes having three colored faces is 8.

Hence, the correct answer is "8".

Shortcut Trick

If a cube has been painted red, blue, and black on pairs of opposite faces and divide it into X parts.

1) Total number of cubes = X3

2) Cubes that have three faces painted = 8 (Because there are only 8 corners in the cube)

3) Cubes which has only two faces painted = (X - 2) × No of Edges (12)

4) Cubes that have only one face painted = (X - 2)2 × 6

5) Cubes which have no face painted = (X - 2)3

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