Calculate Volume: Combining Two Prisms of 6×7×3 and 3×5×4 Meters

To solve this problem, we'll follow these steps:

• Step 1: Calculate the volume of one prism of each type using the formula for volume: $\text{Volume} = \text{length} \times \text{width} \times \text{height}$.
• Step 2: Multiply each result by two since two identical prisms form each body.
• Step 3: Sum the volumes of the two bodies to get the total volume of the combined structure.

Now, let's work through each step:

Step 1: Calculate the volume of Prism 1:
For Prism 1 with dimensions $6 \, \text{m} \times 7 \, \text{m} \times 3 \, \text{m}$, the volume is:

$\text{Volume of one Prism 1} = 6 \times 7 \times 3 = 126 \, \text{m}^3$.

Step 2: Since the body is made from two Prism 1 structures, multiply by 2:

$\text{Total Volume of first body} = 2 \times 126 = 252 \, \text{m}^3$.

Step 3: Calculate the volume of Prism 2:
For Prism 2 with dimensions $3 \, \text{m} \times 5 \, \text{m} \times 4 \, \text{m}$, the volume is:

$\text{Volume of one Prism 2} = 3 \times 5 \times 4 = 60 \, \text{m}^3$.

Since the second body is made from two Prism 2 structures, multiply by 2:

$\text{Total Volume of second body} = 2 \times 60 = 120 \, \text{m}^3$.

Finally, add the two total volumes together to find the volume of the combined structure:

$\text{Total Volume} = 252 + 120 = 372 \, \text{m}^3$.

Therefore, the volume of the resulting body is $372 \, \text{m}^3$.