To informally argue the volume of a pyramid based on the volume of a cube, let's start with our cube, which has a volume of 12 cubic meters.
The formula for the volume of a cube is given by:
\[ V_{\text{cube}} = \text{side length}^3 \]
In this case, the volume of the cube is 12 m³, so we can calculate the side length as follows:
\[ \text{side length} = \sqrt[3]{12} \]
Now let's consider a square-based pyramid that has the same base area and height as this cube. The volume of a pyramid is given by:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{base area} \times \text{height} \]
Since the pyramid has the same base area and height as the cube, we can relate their volumes. The base area of the cube is:
\[ \text{base area of cube} = \text{side length}^2 \]
And the height of the cube is equal to the side length, since it's a cube.
Now, when we calculate the volume of the pyramid using the formula, we realize that it will be one-third the volume of a prism that has the same base area and height (which would be like extending the cube into a rectangular prism).
Since the volume of the cube is 12 m³, the volume of the pyramid, therefore, is:
\[ V_{\text{pyramid}} = \frac{1}{3} \times 12 = 4 \text{ m³} \]
Thus, the volume of the pyramid is 4 m³.
So, the answer is 4 m³ (or 4 m cubed).