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.

1 answer

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.