A cube is painted on all sides and then cut into 'N' smaller cubes. What is the value of 'N' if there are exactly 8 smaller cubes painted on exactly 3 faces?a.27b.124c.Cannot be determinedd.64
Question
A cube is painted on all sides and then cut into 'N' smaller cubes. What is the value of 'N' if there are exactly 8 smaller cubes painted on exactly 3 faces?a.27b.124c.Cannot be determinedd.64
Solution
The answer is a.27. Here's why:
A cube has 8 corners. When a cube is painted on all sides and then cut into smaller cubes, only the smaller cubes that come from the corners will have exactly 3 painted faces. This is because each corner of the cube touches 3 faces.
So, if there are exactly 8 smaller cubes with 3 painted faces, it means the original cube was cut into smaller cubes in such a way that each corner became a smaller cube.
The only way to do this is to make one cut along each axis of the cube (x, y, and z), which divides the cube into 27 smaller cubes (3 cuts along the x-axis, 3 along the y-axis, and 3 along the z-axis gives 3
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