To informally argue for the volume of a pyramid using the volume of a cube, let's start with some basic concepts.
We know that a cube has a volume calculated by multiplying its length, width, and height. In this case, you stated that the volume of the cube is 12 cubic meters.
Now, let's think about the pyramid that has the same base area and height as this cube. The base of the pyramid is a square, just like the bottom face of the cube, and both share the same height.
While a cube occupies its entire volume fully, a pyramid only occupies part of the space above its base. In fact, a pyramid with a square base actually has a volume that is one-third of that of a prism (in this case, our cube) with the same base area and height.
So, if the volume of the cube is 12 cubic meters, we can find the volume of the pyramid by taking one-third of that amount.
Calculating this gives:
\[ \text{Volume of pyramid} = \frac{1}{3} \times \text{Volume of cube} = \frac{1}{3} \times 12 , \text{m}^3 = 4 , \text{m}^3. \]
Thus, the volume of the square-based pyramid is 4 cubic meters.
In terms of the responses, the correct answer is 4 m³ or 4 m cubed.