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

Responses

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

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.

1 answer

The correct response is:

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

This is because the volume of a pyramid is given by the formula:

\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

While the volume of a prism is calculated as:

\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} \]

Since both the prism and the pyramid have congruent triangular bases and the same height, the volume of the pyramid is one-third the volume of the prism.