Question
A large cube with side length 6 cm is painted on all its
faces and then cut into smaller cubes, each with side length 2 cm. How many smaller cubes have only one face painted?Solution
The large cube has a side length of 6 cm, and it is cut into smaller cubes of 2 cm side length. This means the large cube will be cut into 6/2=3cubes along each side, resulting in a total of 3×3×3=27smaller cubes. To find how many cubes have only one face painted, we focus on the cubes at the middle of each face of the large cube. These cubes have one face exposed and painted. Each face of the large cube has 3 x 3 = 9 cubes, and the middle one on each face will have only one face painted. There are 6 faces, so the number of cubes with only one face painted is 6×1=6cubes per face. Therefore, the correct answer is (b), 36.
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