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The problem involves a large cube made of smaller cubes, with some of the small cubes colored black and others white. Specifically, the black cubes form a diagonal line through the large cube, and the remaining small cubes are white. 

The text asks the following questions:

1. If the number of white small cubes accounts for 80% of the total, how many black small cubes are there?
2. If the number of white small cubes is 2024 times that of the black small cubes, how many small cubes are there in total?

Let's break this down step by step:

### Key Information:
- The large cube consists of smaller cubes.
- The black cubes are placed along the diagonal.
- The rest of the cubes are white.
- In the first question, white cubes account for 80% of the total.
- In the second question, the number of white cubes is 2024 times the number of black cubes.

### Steps for Solving:
1. **First Question**:  
   Let the total number of small cubes be \( N \), and the number of black cubes be \( x \).  
   If white cubes account for 80%, then the number of white cubes is \( 0.8N \), and the number of black cubes is \( N - 0.8N = 0.2N \).  
   So, \( x = 0.2N \), meaning 20% of the cubes are black.

2. **Second Question**:  
   The number of white cubes is 2024 times the number of black cubes, so if \( x \) is the number of black cubes, the number of white cubes is \( 2024x \).  
   The total number of cubes would be \( N = x + 2024x = 2025x \).

Let me know if you'd like to go through the calculations or if you have any specific questions! 

Here are 5 related questions for further exploration:
1. How do we calculate the total volume of a large cube based on its side length?
2. What is the formula for determining the number of diagonal cubes in a cube of side \( n \)?
3. How does the percentage of black cubes change if the cube grows larger in dimension?
4. How can we generalize this problem to a 4D hypercube structure?
5. How would the scenario change if each diagonal contained more than one colored cube?

**Tip**: Always double-check your assumptions about percentage distributions in geometry problems, especially when different shapes or orientations are involved.

The problem involves a large cube made of smaller cubes. Some of the smaller cubes along the diagonal are black, and the remaining are white. Questions: (1) If white cubes account for 80% of the total, how many black cubes are there? (2) If the number of white cubes is 2024 times that of black cubes, how many total cubes are there?

Solve a geometry problem involving a large cube with small black and white cubes. Learn how to calculate the total number of cubes based on given ratios and geometric properties. Suitable for students in Grades 7-9.

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