To find the volumes of the prism and the pyramid, we 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 the area of the base and \( h \) is the height.
Since the prism and the pyramid have congruent triangular bases, they share the same base area \( B \).
Let's denote the area of the triangular base as \( B \). The height \( h \) for both shapes is given as 15 m.
Step 1: Calculate the volume of the prism \[ V_{\text{prism}} = B \cdot 15 \]
Step 2: Calculate the volume of the pyramid \[ V_{\text{pyramid}} = \frac{1}{3}B \cdot 15 \]
Now, let's compute the volume using a specific example of base area \( B \). If we assume that the area \( B \) is a certain value, say \( B = 10 , \text{m}^2 \):
For the prism: \[ V_{\text{prism}} = 10 \cdot 15 = 150 , \text{m}^3 \]
For the pyramid: \[ V_{\text{pyramid}} = \frac{1}{3} \cdot 10 \cdot 15 = \frac{150}{3} = 50 , \text{m}^3 \]
Final Answers:
- The volume of the prism is 150 m³.
- The volume of the pyramid is 50 m³.
You can use any area for the base \( B \) to get the corresponding volumes as long as the proportions remain consistent.