A rectangular prism has a volume of 252 in.3

. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?(1

1 answer

The volume \( V \) of a rectangular prism is given by the formula:

\[ V = \text{Base Area} \times \text{Height} \]

For a rectangular pyramid, the volume is calculated using the formula:

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

Since the pyramid has a base and height that are congruent to the rectangular prism, we can use the same base area and height. Given that the volume of the rectangular prism is \( 252 , \text{in}^3 \), we can express the volume of the pyramid in relation to the volume of the prism.

Substituting the volume of the prism into the formula for the volume of the pyramid:

\[ V_{\text{pyramid}} = \frac{1}{3} \times 252 \]

Calculating this gives:

\[ V_{\text{pyramid}} = \frac{252}{3} = 84 , \text{in}^3 \]

Thus, the volume of the pyramid is

\[ \boxed{84 , \text{in}^3} \]