To find the volume of a pyramid that has the same base area and height as a given prism, you can use the relationship between the volume of a prism and the volume of a pyramid.
The volume \( V \) of a prism is calculated using the formula: \[ V_{\text{prism}} = B \cdot h \] where \( B \) is the area of the base, and \( h \) is the height.
The volume \( V \) of a pyramid is calculated using the formula: \[ V_{\text{pyramid}} = \frac{1}{3} B \cdot h \] where \( B \) is again the area of the base, and \( h \) is the height.
If you know the volume of the prism is 600, you can express it as: \[ 600 = B \cdot h \]
To find the volume of the pyramid that has the same base and height, substitute into the pyramid's volume formula: \[ V_{\text{pyramid}} = \frac{1}{3} (B \cdot h) \]
Now we can use the known volume of the prism: \[ V_{\text{pyramid}} = \frac{1}{3} \cdot 600 \] \[ V_{\text{pyramid}} = 200 \]
So, the volume of the pyramid with the same base and height as the given prism would be 200.