To find the density of a honeycomb mesh per square meter, we need to know the weight of the material per unit area. Since the question doesn't specify the material density or weight, I'll walk through the steps assuming you're looking for the theoretical weight of the mesh itself based on the given dimensions.

### Given:
- **Side length of the hexagonal cell** (\( s \)) = 8 mm = 0.008 m
- **Wall thickness** = 0.08 mm = 0.00008 m
- **Area to be covered** = 1 m²

### Steps to Calculate Density:

1. **Calculate the area of one hexagonal cell**:
   The area of a regular hexagon can be calculated as:
   \[
   A_{\text{hex}} = \frac{3\sqrt{3}}{2} \times s^2
   \]
   Substituting \( s = 0.008 \) m:
   \[
   A_{\text{hex}} = \frac{3\sqrt{3}}{2} \times (0.008)^2 \approx 0.000000166 \text{ m}^2
   \]

2. **Calculate the number of cells in 1 m²**:
   \[
   \text{Number of cells} = \frac{1 \text{ m}^2}{A_{\text{hex}}} = \frac{1}{0.000000166} \approx 6,000,000 \text{ cells}
   \]

3. **Calculate the perimeter of one hexagonal cell**:
   The perimeter of a hexagon is:
   \[
   P = 6 \times s = 6 \times 0.008 = 0.048 \text{ m}
   \]

4. **Calculate the length of the walls per cell**:
   Since the wall thickness is \( t = 0.00008 \) m, the volume of the material used for one cell's walls is:
   \[
   V_{\text{wall}} = P \times t \times \text{height (assume 1 m for simplicity)}
   \]
   \[
   V_{\text{wall}} = 0.048 \times 0.00008 \times 1 = 0.00000384 \text{ m}^3
   \]

5. **Calculate the total volume of material in 1 m²**:
   Multiply the volume per cell by the number of cells:
   \[
   V_{\text{total}} = V_{\text{wall}} \times \text{Number of cells} = 0.00000384 \times 6,000,000 = 23.04 \text{ m}^3
   \]

6. **Calculate the density**:
   Assuming the material has a specific density \( \rho \) (e.g., aluminum has \( \rho \approx 2700 \) kg/m³), the total mass is:
   \[
   \text{Mass} = V_{\text{total}} \times \rho = 23.04 \times 2700 = 62112 \text{ kg}
   \]
   Finally, the density for 1 m² area of the mesh is:
   \[
   \text{Density per m²} = \frac{\text{Mass}}{1 \text{ m}^2} = 62112 \text{ kg/m}^2
   \]

**Note**: The actual density will vary depending on the material and whether the mesh is filled or empty. This calculation is based on a simplified model assuming the honeycomb is solid material.

### Questions to Explore Further:
1. How does the density change if the wall thickness is reduced by half?
2. What would be the density for a honeycomb mesh made of steel?
3. How does the density compare for a filled versus an unfilled honeycomb mesh?
4. What are practical applications where honeycomb meshes are used for their lightweight properties?
5. How would increasing the side length of the cells affect the overall density?

### Tip:
Always consider the material properties and geometric factors when calculating density, as these will have a significant impact on the final value.

Learn how to calculate the density of a honeycomb mesh per square meter with a detailed step-by-step solution. This problem involves geometry and material density calculations based on the dimensions of the hexagonal cells and wall thickness. Suitable for advanced level learners and engineering enthusiasts.

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