Understanding the Cube Division Problem

This problem involves a large cube that is cut into smaller identical cubes. To find the number of small cubes obtained, we can use the concept of volume. The total volume of the large cube remains constant, even when it's divided into smaller pieces. Therefore, the total volume is simply the sum of the volumes of all the smaller cubes.

Calculating the Volume of the Cubes

First, let's find the volume of the large cube. The side of the large cube is given as 4 cm.

Volume of a cube is calculated using the formula: \( \text{Volume} = \text{side}^3 \)

Volume of the large cube: \( (4 \text{ cm})^3 = 4 \times 4 \times 4 \text{ cm}^3 = 64 \text{ cm}^3 \)

Next, let's find the volume of one small cube. The side of each small cube is given as 2 cm.

Volume of a small cube: \( (2 \text{ cm})^3 = 2 \times 2 \times 2 \text{ cm}^3 = 8 \text{ cm}^3 \)

Finding the Number of Small Cubes

To find the total number of small cubes obtained, we divide the volume of the large cube by the volume of a single small cube.

Number of small cubes = \( \frac{\text{Volume of large cube}}{\text{Volume of small cube}} \)

Number of small cubes = \( \frac{64 \text{ cm}^3}{8 \text{ cm}^3} \)

Number of small cubes = \( 8 \)

Thus, when a cube of side 4 cm is divided into smaller cubes of side 2 cm each, 8 small cubes are obtained.

The information about the cube being painted green is relevant for problems asking about the number of cubes with painted faces (like 3 faces painted, 2 faces painted, etc.), but for finding the total number of small cubes, only the dimensions matter.