Calculate Volume of Combined Cuboids: 3x4x7 Meter Orthohedra Assembly

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

• Step 1: Calculate the volume of a single cuboid using the dimensions provided.
• Step 2: Multiply the volume of one cuboid by the number of cuboids to find the total volume of the assembled body.

Let's work through each step:

Step 1: The dimensions of the given cuboid are 3 meters, 4 meters, and 7 meters. The volume of this cuboid is calculated using the formula:

$\text{Volume of one cuboid} = \text{length} \times \text{width} \times \text{height} = 3 \times 4 \times 7$

Performing the calculation:

$3 \times 4 = 12$

$12 \times 7 = 84$

Therefore, the volume of one cuboid is $84 \text{ cubic meters}$.

Step 2: Since there are three identical cuboids combined to form the body, we multiply the volume of one cuboid by 3:

$\text{Total Volume} = 84 \times 3$

Carrying out the multiplication:

$84 \times 3 = 252$

Therefore, the volume of the created body is $\text{252 cubic meters}$.

Thus, the correct answer is $252$, which matches choice 3 in the given options.