A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?
Explanation:
Since each side of the smaller cube is 3 cm, it can be figured out that each face of the original cube is divided into 4 parts, or in other words, the original cube is divided into 64 smaller cubes. For a smaller cube to have none of its sides painted, it should not be a part of the face of the original cube (i.e. none of its faces should be exposed).
We can find at the centre of the original cube there are (2 × 2 × 2) = 8 such cubes.
Hint:
Students please note that the answer can only be a cube of some integer. The only cube among the answer choices is (2)3 = 8.
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