A 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 cube and how it is divided into smaller cubes.

Step 1: Visualize the cube Imagine a standard cube with six faces. Two opposite faces are painted yellow, another two opposite faces are painted orange, and the remaining two faces are painted white.

Step 2: Divide the cube The cube is cut into 343 smaller but identical cubes. This means that the original cube is divided into 7 smaller cubes along each edge (7 x 7 x 7 = 343).

Step 3: Count the cubes with exactly one color To determine how many of the smaller cubes have exactly one color on them, we need to consider the different possibilities.

• Yellow cubes: Each yellow face of the original cube is divided into 7 smaller cubes along each edge. So, there are 7 x 7 = 49 yellow cubes.
• Orange cubes: Similarly, each orange face is divided into 7 smaller cubes along each edge. Therefore, there are 7 x 7 = 49 orange cubes.
• White cubes: The remaining faces, which are painted white, are also divided into 7 smaller cubes along each edge. Hence, there are 7 x 7 = 49 white cubes.

Step 4: Calculate the total number of cubes with exactly one color To find the total number of cubes with exactly one color, we add up the number of yellow, orange, and white cubes: 49 + 49 + 49 = 147.

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