To find the volumes of the prism and the pyramid, we can use the following formulas:
-
Volume of a Prism:
\[ V = B \cdot h \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height. -
Volume of a Pyramid:
\[ V = \frac{1}{3} B \cdot h \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
Let’s denote the area of the triangular base as \( B \). Since both the prism and the pyramid share the same base and height:
- The height \( h \) is given as 15 m.
Now we can express their volumes:
-
Volume of the Prism:
\[ V_{\text{prism}} = B \cdot 15 \] -
Volume of the Pyramid:
\[ V_{\text{pyramid}} = \frac{1}{3} B \cdot 15 \]
\[ V_{\text{pyramid}} = 5B \]
So, we need the area \( B \) to calculate specific volumes. Without a specific numerical value for the area \( B \), we can express the volumes in terms of \( B \).
Therefore:
- Volume of the prism: \( 15B \) m³
- Volume of the pyramid: \( 5B \) m³
If you know the area of the triangular base \( B \), you can substitute that value to find the concrete volume measurements.