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How many small cubes do we need to complete the main cube?

To determine the number of small cubes required to complete the main cube, we first need to understand the structure. 

The given figure represents a 3D structure composed of small cubes. To solve this, let's break it down:

1. **Determine the size of the main cube**: 
   - The main cube is \(4 \times 4 \times 4\) in dimensions, so the total number of cubes in a complete structure would be \(4^3 = 64\) small cubes.

2. **Count the number of cubes present in the current structure**:
   - We can count the number of visible cubes layer by layer from bottom to top:
     - **Bottom layer**: 9 cubes
     - **Second layer**: 6 cubes
     - **Third layer**: 4 cubes
     - **Top layer**: 1 cube

   Adding these up: \(9 + 6 + 4 + 1 = 20\) cubes are currently present.

3. **Calculate the missing cubes**:
   - The difference between the total cubes in a complete structure and the current structure gives us the number of missing cubes: 
   \[
   64 - 20 = 44
   \]

So, **44 small cubes** are needed to complete the main cube.

Would you like any further details or explanations?

Here are some related questions you might find interesting:

1. What is the formula for calculating the volume of a cube?
2. How many cubes are needed to build a \(5 \times 5 \times 5\) cube?
3. How can we calculate the surface area of the current incomplete structure?
4. If each small cube has a side length of 2 cm, what would be the total surface area of the completed cube?
5. How does the number of visible faces change as layers are added?

**Tip**: When counting cubes in a 3D structure, it's helpful to break the structure down into layers to ensure accuracy.

Learn how to calculate the number of small cubes needed to complete a 4x4x4 cube structure. Understand the concept of volume in 3D shapes and how to count cubes layer by layer. Suitable for Grades 6-8.

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