To find the volume of the square-based pyramid, we first need to establish the relationship between the volume of the cube and the pyramid.
The volume \( V \) of a cube is given by the formula: \[ V = s^3 \] where \( s \) is the length of a side of the cube. Given that the volume of the cube is 30 cubic meters, we have: \[ s^3 = 30 \] To find the side length \( s \), we take the cube root: \[ s = \sqrt[3]{30} \]
The volume \( V \) of a square-based pyramid is given by the formula: \[ V = \frac{1}{3} \times \text{base area} \times \text{height} \] For a square-based pyramid with the same base as the cube, the base area \( A \) is: \[ A = s^2 \] The height \( h \) of the pyramid is equal to the side length \( s \) of the cube.
Now, substituting the base area and height into the pyramid volume formula, we have: \[ V = \frac{1}{3} \times s^2 \times s = \frac{1}{3} \times s^3 \] Since we know \( s^3 = 30 \): \[ V = \frac{1}{3} \times 30 = 10 \]
Therefore, the volume of the pyramid is 10 cubic meters.
The correct response is: 10 cubic meters.