To calculate the volumes of the prism and the pyramid with congruent triangular bases and the same height, you can use the following formulas:
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Volume of a Prism: \[ V = B \cdot h \] where \( B \) is the area of the base, and \( h \) is the height.
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Volume of a Pyramid: \[ V = \frac{1}{3} B \cdot h \] where \( B \) is again the area of the base, and \( h \) is the height.
Since the heights of both shapes are the same (15 m), we need to find the area of the triangular base.
Let \( B \) be the area of the triangular base (we’ll need to calculate that or assume a value).
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For the prism: \[ V_{\text{prism}} = B \cdot 15 \]
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For the pyramid: \[ V_{\text{pyramid}} = \frac{1}{3} B \cdot 15 \]
Now we can compare the two volumes:
- The volume of the prism is \( 15B \) m³.
- The volume of the pyramid is \( 5B \) m³.
Now, if we had a specific value for \( B \) (the area of the triangular base), we could substitute it in and get numeric volumes. However, we only need to provide the formulas in terms of \( B \).
Therefore, assuming we don't have the specific area of the base, we can summarize:
The volume of the prism is \( 15B \) m³.
The volume of the pyramid is \( 5B \) m³.