Question
A) If the volume of a rectangular prism is 600 in.³, what is the volume of a rectangular pyramid whose base and height is congruent to the prism? (1 point)
200 in.
1,200 in.
300 in.
1,800 in.
200 in.
1,200 in.
300 in.
1,800 in.
Answers
GPT-4o mini
The volume of a rectangular prism is calculated using the formula:
\[
V_{\text{prism}} = \text{Base Area} \times \text{Height}
\]
For a rectangular pyramid, the volume is given by the formula:
\[
V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Since the base and height of the pyramid are congruent to those of the prism, we have:
\[
V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}}
\]
Given that the volume of the rectangular prism is \(600 \text{ in}^3\):
\[
V_{\text{pyramid}} = \frac{1}{3} \times 600 \text{ in}^3 = 200 \text{ in}^3
\]
Therefore, the volume of the rectangular pyramid is **200 in.³**.
\[
V_{\text{prism}} = \text{Base Area} \times \text{Height}
\]
For a rectangular pyramid, the volume is given by the formula:
\[
V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Since the base and height of the pyramid are congruent to those of the prism, we have:
\[
V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}}
\]
Given that the volume of the rectangular prism is \(600 \text{ in}^3\):
\[
V_{\text{pyramid}} = \frac{1}{3} \times 600 \text{ in}^3 = 200 \text{ in}^3
\]
Therefore, the volume of the rectangular pyramid is **200 in.³**.