Question
There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3
, what is the volume of the prism?(1 point)
Responses
16 in.3
16 in. cubed
24 in.3
24 in. cubed
144 in.3
144 in. cubed
96 in.3
, what is the volume of the prism?(1 point)
Responses
16 in.3
16 in. cubed
24 in.3
24 in. cubed
144 in.3
144 in. cubed
96 in.3
Answers
Answered by
GPT-4o mini
The volume of a pyramid is given by the formula:
\[
V_{pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The volume of a rectangular prism (or box) is given by the formula:
\[
V_{prism} = \text{Base Area} \times \text{Height}
\]
Since the pyramid and prism have congruent bases and heights, we can express the volume of the prism in terms of the volume of the pyramid. Specifically, the volume of the prism is three times that of the pyramid, because:
\[
V_{prism} = 3 \times V_{pyramid}
\]
Given that the volume of the pyramid is \(48 \, \text{in}^3\), we can calculate the volume of the prism:
\[
V_{prism} = 3 \times 48 \, \text{in}^3 = 144 \, \text{in}^3
\]
Therefore, the volume of the prism is:
\[
\boxed{144 \, \text{in}^3}
\]
\[
V_{pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
The volume of a rectangular prism (or box) is given by the formula:
\[
V_{prism} = \text{Base Area} \times \text{Height}
\]
Since the pyramid and prism have congruent bases and heights, we can express the volume of the prism in terms of the volume of the pyramid. Specifically, the volume of the prism is three times that of the pyramid, because:
\[
V_{prism} = 3 \times V_{pyramid}
\]
Given that the volume of the pyramid is \(48 \, \text{in}^3\), we can calculate the volume of the prism:
\[
V_{prism} = 3 \times 48 \, \text{in}^3 = 144 \, \text{in}^3
\]
Therefore, the volume of the prism is:
\[
\boxed{144 \, \text{in}^3}
\]