A Rectangular prism has a volume of 252 in3 If a rectangular pyramid has a base and height congruent 2 da prism, wut is da volume of da pyramid

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1 answer

The volume \( V \) of a rectangular prism can be calculated using the formula:

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

Given that the volume of the rectangular prism is 252 in³, we can denote the base area as \( A \) and the height as \( h \):

\[ A \times h = 252 \text{ in}^3 \]

For a rectangular pyramid with a base area and height congruent to that of the prism, the volume \( V \) of the pyramid is calculated using the formula:

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

Substituting the base area \( A \) and height \( h \) from the prism's volume:

\[ V = \frac{1}{3} \times A \times h \]

Since we know that \( A \times h = 252 \text{ in}^3 \):

\[ V = \frac{1}{3} \times 252 \text{ in}^3 \]

Calculating this gives:

\[ V = \frac{252}{3} = 84 \text{ in}^3 \]

Thus, the volume of the pyramid is

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