If a prism and a pyramid have congruent triangular bases and the same heights, then(1 point)

Responses

the volume of the prism is 13
the size of the volume of the pyramid.
the volume of the prism is Start Fraction 1 over 3 End Fraction the size of the volume of the pyramid.

the volume of the pyramid and the volume of the prism are the same.
the volume of the pyramid and the volume of the prism are the same.

the volume of the pyramid is three times as large as the volume of the prism.
the volume of the pyramid is three times as large as the volume of the prism.

the volume of the pyramid is 13
the size of the volume of the prism.

1 answer

The correct response is:

the volume of the prism is 3 times the size of the volume of the pyramid.

The volume of a prism can be 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 of a pyramid is calculated using the formula:

\[ V_{\text{pyramid}} = \frac{1}{3} B \cdot h \]

So, if they have congruent triangular bases and the same height, the volume of the prism will be three times that of the pyramid. Therefore, the relationship between the volumes is:

\[ V_{\text{prism}} = 3 \cdot V_{\text{pyramid}} \]