pair of opposite faces of a cube is painted yellow another pair of opposite faces orange and the remaining faces white. The cube is then cut in to 343 smaller but identical cubes.How many of the smaller cubes have exactly one colour on them?     a.144                b.150           c.125           d.130

To solve this problem, we need to understand the structure of the original cube and how it is divided into smaller cubes.

The original cube has 6 faces. One pair of opposite faces is painted yellow, another pair is painted orange, and the remaining faces are painted white. This means that there are 2 yellow faces, 2 orange faces, and 2 white faces.

When the cube is cut into smaller cubes, each smaller cube will have one face exposed. Let's consider the different possibilities for the exposed face:

1. Yellow face: There are 2 yellow faces in the original cube. Since all the smaller cubes are identical, each yellow face will be exposed by 7 smaller cubes (one in the center and 6 surrounding it). So, there will be a total of 2 * 7 = 14 smaller cubes with a yellow face.

2. Orange face: Similarly, there are 2 orange faces in the original cube. Each orange face will also be exposed by 7 smaller cubes. Therefore, there will be a total of 2 * 7 = 14 smaller cubes with an orange face.

3. White face: Finally, there are 2 white faces in the original cube. Each white face will be exposed by 5 smaller cubes (one in the center and 4 surrounding it). So, there will be a total of 2 * 5 = 10 smaller cubes with a white face.

To find the total number of smaller cubes with exactly one color on them, we add up the number of cubes with each color: 14 + 14 + 10 = 38.

Therefore, the correct answer is not provided in the options given.