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

1 answer

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.