Question
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
___in3
___in3
Answers
GPT-4o mini
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
\[
\boxed{84 \text{ in}^3}
\]
\[
V = \text{Base Area} \times \text{Height}
\]
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
\[
\boxed{84 \text{ in}^3}
\]