A prism and a pyramid have congruent triangular basis. If their heights are both 15 m what is the volume of each shape

Answer 1

The volume \(V\) of a prism is given by the formula:
\[ V = A \cdot h \]
where \(A\) is the area of the base and \(h\) is the height.

Since the triangular bases of the prism and the pyramid are congruent, the area of the base is the same for both shapes. Let's denote the area of the triangular base as \(B\).

For the prism:
\[ V_{\text{prism}} = B \cdot 15 \]

For the pyramid:
The volume of a pyramid is given by the formula:
\[ V = \frac{1}{3} \cdot B \cdot h \]

Plugging in the values:
\[ V_{\text{pyramid}} = \frac{1}{3} \cdot B \cdot 15 \]

Since the bases are congruent, the volumes of the prism and the pyramid are the same. We can set the two equations equal to each other and solve for \(B\):
\[ B \cdot 15 = \frac{1}{3} \cdot B \cdot 15 \]
\[ B = \frac{1}{3} \cdot B \]
\[ 3B = B \]
\[ B = 0 \]

This result indicates that the area of the base is 0, which would not make geometric sense. This implies that there may be an error in the information given or some assumption made.