125 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces2.How many of the smaller cubes have exactly one face painted?

To find out how many of the smaller cubes have exactly one face painted, we need to analyze the structure of the larger cube.

Since the larger cube is formed by putting together 125 smaller identical cubes, we know that it has a length, width, and height of 5 smaller cubes each (since 5 x 5 x 5 = 125).

Now, let's consider the cubes on the outer layer of the larger cube. These cubes will have exactly one face painted, as they are exposed to the exterior of the larger cube.

To calculate the number of cubes on the outer layer, we need to find the total number of cubes on the surface of the larger cube. Since the larger cube has 6 faces, each face will have a dimension of 5 x 5 (since it is made up of 5 smaller cubes in each row and column).

Therefore, the total number of cubes on the surface of the larger cube is 6 x (5 x 5) = 150.

However, we need to subtract the 4 corner cubes, as they are counted twice (once for each adjacent face). So, we subtract 4 from 150, which gives us 146 cubes on the outer layer.

Since each cube on the outer layer has exactly one face painted, the number of smaller cubes with exactly one face painted is 146.

Therefore, there are 146 smaller cubes that have exactly one face painted.