Solid cube of 6 * 6 * 6. This cube is cut into to 216 small cubes. (1 * 1 * 1).the big cube is painted in all its faces. Then how many of cubes are painted at least 2 sides ?

To solve this question, let's consider the different types of small cubes that can be formed when the big cube is cut.

The big cube is made up of 6 x 6 x 6 = 216 small cubes.

1. The corner small cubes: There are 8 corner small cubes in the big cube. Each corner small cube has 3 faces painted.
2. The edge small cubes: There are 12 edges in the big cube, with each edge consisting of 6 small cubes. So, there are a total of 12 x 6 = 72 edge small cubes. Each edge small cube has 2 faces painted.
3. The face small cubes: The big cube has 6 faces, each consisting of 6 x 6 = 36 small cubes. So, there are a total of 6 x 36 = 216 face small cubes. Each face small cube has 1 face painted.

Now, let's calculate the number of small cubes that are painted on at least 2 sides:

1. Corner small cubes: 8 x 3 = 24 cubes (since each corner small cube has 3 faces painted).
2. Edge small cubes: 72 x 2 = 144 cubes (since each edge small cube has 2 faces painted).
3. Face small cubes: 216 x 1 = 216 cubes (since each face small cube has 1 face painted).

So, the total number of small cubes painted on at least 2 sides is 24 + 144 + 216 = 384.

Therefore, the correct answer is A) 56.

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