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Question

A cube is painted on all its faces and then cut into 27 smaller cubes. How many smaller cubes will have exactly 3 faces painted?

The correct answer is

8

To determine how many smaller cubes will have exactly 3 faces painted, we need to understand the structure of the cube after being cut. Initially, a larger cube is divided into 27 smaller cubes, implying it is a 3x3x3 cube.
Each of these 27 smaller cubes can have different numbers of faces painted (0, 1, 2, or 3 faces painted).
The smaller cubes with exactly 3 faces painted are located at the corners of the original cube. These corner cubes are distinct because each one is at the intersection of three faces of the larger cube.
In a cube, there are always 8 corners, hence there are 8 smaller cubes that will have exactly 3 faces painted.
Therefore, the number of smaller cubes with exactly 3 faces painted is 8.
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Important Questions from Miscellaneous (APSC)

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