To solve this problem, we need to use the fact that the two cubes are similar. For similar cubes, the ratio of their volumes is the cube of the ratio of their corresponding side lengths.

Let’s proceed step-by-step:

1. Ratio of side lengths: The width (or side length) of the first cube is 60 cm, and the width of the second cube is 240 cm. So, the ratio of their side lengths is: $\frac{240}{60} = 4$

2. Cube of the ratio: The volumes of similar cubes are proportional to the cubes of their side lengths. Thus, the volume ratio will be: $4^3 = 64$

3. Finding the volume of the second cube: The volume of the first cube is given as 36,000 cm³. Therefore, the volume of the second cube will be 64 times this: $\text{Volume of the second cube} = 36,000 \times 64 = 2,304,000 \, \text{cm}^3$

Thus, the volume of the second cube is 2,304,000 cm³.

Would you like more details on any of the steps?

Here are 5 related questions:

1. What is the relationship between surface area and side length for similar cubes?
2. If the side length of a cube is doubled, how does the surface area change?
3. How can you derive the formula for the volume of a cube?
4. If two shapes are similar but not cubes, how does the volume ratio relate to their side length ratio?
5. What is the surface area of the second cube?

Tip: When dealing with similar shapes, remember that areas scale with the square of the side length ratio, and volumes scale with the cube of the side length ratio.