Question
There is a rectangular prism n pyramid with congruent bases n height. if da volume of da pyramid is 48 in3, wut is da volume of da prism?
A ) 96 in 3
B ) 16 in 3
C ) 24 in 3
D ) 144 in 3
A ) 96 in 3
B ) 16 in 3
C ) 24 in 3
D ) 144 in 3
Answers
GPT-4o mini
To find the volume of the rectangular prism when given the volume of a pyramid with congruent bases and the same height, we can use the formula for the volume of both shapes.
The volume \( V \) of a pyramid is given by the formula:
\[
V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The volume \( V \) of a prism is given by:
\[
V_{\text{prism}} = \text{Base Area} \times \text{Height}
\]
Since the pyramid has the same base area and height as the prism, we can express the relationship between their volumes:
\[
V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}}
\]
Given that the volume of the pyramid is \( 48 \, \text{in}^3 \), we can set up the equation:
\[
48 = \frac{1}{3} \times V_{\text{prism}}
\]
To find the volume of the prism, multiply both sides by 3:
\[
V_{\text{prism}} = 48 \times 3 = 144 \, \text{in}^3
\]
Therefore, the volume of the prism is:
\[
\boxed{144 \, \text{in}^3}
\]
The answer is (D) 144 in³.
The volume \( V \) of a pyramid is given by the formula:
\[
V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The volume \( V \) of a prism is given by:
\[
V_{\text{prism}} = \text{Base Area} \times \text{Height}
\]
Since the pyramid has the same base area and height as the prism, we can express the relationship between their volumes:
\[
V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}}
\]
Given that the volume of the pyramid is \( 48 \, \text{in}^3 \), we can set up the equation:
\[
48 = \frac{1}{3} \times V_{\text{prism}}
\]
To find the volume of the prism, multiply both sides by 3:
\[
V_{\text{prism}} = 48 \times 3 = 144 \, \text{in}^3
\]
Therefore, the volume of the prism is:
\[
\boxed{144 \, \text{in}^3}
\]
The answer is (D) 144 in³.