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To solve the problem, let's break it down step by step.

### Problem Recap:
- A metal frame is made by welding together four bars of steel.
- Each bar has a cross-sectional area of \( 4.2 \, \text{cm}^2 \).
- The dimensions of the frame are 27 cm in length and 19 cm in height.
- We need to find the volume of metal used in making the frame.

### Steps to Solve:

1. **Determine the total length of the bars**:
   - The frame is rectangular, so it has two vertical bars and two horizontal bars.
   - Each vertical bar is 19 cm long.
   - Each horizontal bar is 27 cm long.

   \[
   \text{Total length} = 2 \times 27 \, \text{cm} + 2 \times 19 \, \text{cm}
   \]
   \[
   \text{Total length} = 54 \, \text{cm} + 38 \, \text{cm} = 92 \, \text{cm}
   \]

2. **Calculate the volume of the metal**:
   - The volume of each bar can be calculated using the formula:
   \[
   \text{Volume} = \text{Cross-sectional area} \times \text{Length}
   \]
   - Therefore, the total volume \( V \) is:
   \[
   V = 4.2 \, \text{cm}^2 \times 92 \, \text{cm}
   \]

   Let's calculate this:

   \[
   V = 386.4 \, \text{cm}^3
   \]

### Conclusion:
The volume of metal used in making the frame is approximately **386.4 cm³**.

Would you like further details or explanations on this solution?

Here are 5 related questions you might find interesting:
1. How would the volume change if the cross-sectional area was doubled?
2. What would the volume be if the dimensions of the frame were doubled?
3. How does the thickness of the bars affect the overall weight of the frame?
4. Can you calculate the surface area of the metal frame?
5. What is the impact of using a different material with a higher density on the weight of the frame?

**Tip:** When calculating volumes or areas, always ensure your units are consistent throughout the problem to avoid errors.

Discover how to calculate the volume of a metal frame made from welded steel bars using geometry principles. This problem involves finding the volume of a rectangular prism based on given dimensions and cross-sectional area. Suitable for Grades 7-9 students studying geometry and volume calculations.

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