Calculate Volume: Three 5×7 Orthohedra Forming Composite Shape

To solve this problem of calculating the volume of a new shape formed by three identical cuboids, we need to follow these steps:

• Step 1: Calculate the volume of a single cuboid.
• Step 2: Multiply the volume of one cuboid by the number of cuboids (three) to get the total volume.

Let's work through these steps:

Step 1: The volume of a single cuboid is calculated using the formula for the volume of a cuboid, which is:
$V = \text{length} \times \text{width} \times \text{height}$

Given that the length and width are $5$ meters and $7$ meters, and assuming the height (expected to be the same as the base's side since it's square-based and not otherwise specified) is another $5$, we have:
$V_{\text{cuboid}} = 5 \times 7 \times 5 = 175 \, \text{m}^3$

Step 2: Multiply the volume of one cuboid by three because there are three identical cuboids:
$V_{\text{total}} = 3 \times 175 = 525 \, \text{m}^3$

Therefore, the volume of the new shape is $\mathbf{525} \, \text{m}^3$.