Question
A cube of side length 5 cm is painted on all its faces
and then cut into smaller cubes of side length 1 cm. How many smaller cubes have no paint on them?Solution
The large cube has a side length of 5 cm, and it is cut into smaller cubes with side length 1 cm. The number of smaller cubes created is (5/1) ×(5/1) ×(5/1) =125smaller cubes in total. The smaller cubes that have no paint on them are those in the center of the large cube. These cubes are completely surrounded by other cubes and are not exposed to any painted faces. To find the number of cubes with no paint, we consider the smaller cube formed in the center, which has side length 3 cm (since the cubes on the outer layer have paint). Thus, the number of smaller cubes with no paint on them is 3×3×3=27. Therefore, the correct answer is (b), 27.
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