Final answer:
In a 3x3x3 cube composed of 27 smaller cubes, there are 6 smaller cubes that have only one painted face, specifically the center cube on each of the six faces.
Step-by-step explanation:
A student asked how many smaller cubes with only one painted face are there in a larger cube made of 27 smaller cubes. To solve this, we need to consider the structure of the larger cube. Since the larger cube consists of 27 smaller cubes, we can deduce that it is a 3 x 3 x 3 cube. The smaller cubes with only one painted face would be the ones on the faces of the larger cube but not on the edges or corners.
Each face of the cube will have only the center cube with one painted face, since the edge cubes will have two painted faces, and the corner cubes will have three painted faces. There are 6 faces on a cube, so we can calculate this by taking 6 (faces) × 1 (center cube per face) = 6 smaller cubes with only one painted face each.