To solve the problem, we first need to find the side length of the cube using its volume.
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 450 cubic feet, we have: \[ s^3 = 450. \] To find \( s \), we calculate: \[ s = \sqrt[3]{450} \approx 7.6 \text{ feet}. \]
Now, the base area \( A \) of the cube (which is also the area of its base) is: \[ A = s^2 = (7.6)^2 \approx 57.76 \text{ square feet}. \]
Since the cube and the square-based pyramid have the same base area and height, we can also calculate the volume of the square-based pyramid. The volume \( V \) of a pyramid is given by: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height}. \]
The height of the cube is also \( s \), which is approximately \( 7.6 \) feet. Therefore, the volume of the pyramid becomes: \[ V = \frac{1}{3} \times A \times s, \] where \( A = 57.76 \) square feet, and \( s \approx 7.6 \) feet.
Now substitute values: \[ V = \frac{1}{3} \times 57.76 \times 7.6. \] Calculating this: \[ V = \frac{1}{3} \times 438.176 \approx 146.059 \text{ cubic feet}. \]
Thus, rounding it leads us to a volume of approximately \( 150 \) cubic feet.
The volume of the pyramid is 150 ft³. Thus, the correct response is: 150 ft³.