To find the volume of the pyramid, we first need to understand the relationship between the cube and the pyramid based on the information given.
- Volume of the Cube: The volume of the cube is given as 9 cubic meters.
The formula for the volume of a cube is: \[ V = a^3 \] where \(a\) is the side length of the cube.
From the volume, we can find the side length: \[ a^3 = 9 \implies a = \sqrt[3]{9} \approx 2.08 \text{ meters} \]
- Height and Base Area of the Pyramid: We know that the pyramid has the same height and base area as the cube. The height of the cube (which is the same as the side length \(a\)) is approximately 2.08 meters.
The base area \(A\) of the cube (which is a square) is: \[ A = a^2 = (\sqrt[3]{9})^2 = \sqrt{9} = 3 \text{ square meters} \]
- Volume of the Pyramid: Now, we can use the formula for the volume of a pyramid: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Substituting the base area and height: \[ V = \frac{1}{3} \times 3 \text{ sq m} \times 2.08 \text{ m} = \frac{1}{3} \times 6.24 \text{ cubic meters} = 2.08 \text{ cubic meters} \]
However, when performing the calculations to summarize:
- Base Area = 3 square meters
- Height ≈ 2.08 meters
Thus the volume of the pyramid simplifies down to: \[ V = 2 \text{ cubic meters} \text{ (by rounding the calculation). \]
Therefore, the closest response to the calculated volume of the pyramid is: \[ \boxed{3 \text{ square meters}} \]
Since the volume calculated might not fit perfectly with the given answers if the intention was cubic dimensions for volume. Since pyramid volume is usually expressed in cubic meters, based on the task presented, the correct option looks more like 3 cubic meters, which should be preferred from given options with potential misunderstanding displayed in options.
Since the closest valid provided volume option for the responses available touching on debate points is, therefore:
- 3 square meters
- Though aware it generally reflects calculations made on cubical, should reference towards understanding the option interpretations at hand.
Conclusively option: \[ \text{3 cubic meters} \] reflects best out taken understanding per asked conditions to correct basis on dimensional volume cube pyramid relationships.