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 point)
 in.3

1 answer

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

\[ V = \text{length} \times \text{width} \times \text{height} \]

For a rectangular pyramid, the volume \( V \) is given by the formula:

\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]

If the pyramid has a base and height congruent to the prism, then the base area will be the same as the base area of the prism, and the height will also be the same. Therefore, the volume of the pyramid can be calculated as:

\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{base area} \times \text{height} \]

Since the volume of the prism is already known to be \( 252 , \text{in}^3 \), we can express the volume of the pyramid in terms of the volume of the prism:

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

Substituting the volume of the prism:

\[ V_{\text{pyramid}} = \frac{1}{3} \times 252 , \text{in}^3 = 84 , \text{in}^3 \]

Thus, the volume of the pyramid is:

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