To find the volume of a rectangular pyramid with a base and height congruent to a rectangular prism, we can use the formulas for the volumes of both shapes.
-
The volume \( V \) of a rectangular prism is given by the formula: \[ V = \text{length} \times \text{width} \times \text{height} \] In this case, we know that the volume of the rectangular prism is 600 in³.
-
The volume \( V \) of a rectangular pyramid is given by the formula: \[ V = \frac{1}{3} \times \text{base area} \times \text{height} \] The base area of the pyramid is the same as the base area of the prism. Therefore, we can express the base area as: \[ \text{base area} = \text{length} \times \text{width} \]
-
Since the height of the pyramid is the same as the height of the prism, we can denote the height as \( h \).
-
Now substituting the base area and height into the pyramid volume formula, we get: \[ V_{\text{pyramid}} = \frac{1}{3} \times (\text{length} \times \text{width}) \times h \] This can also be expressed as: \[ V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}} \]
-
Therefore, substituting the volume of the prism, we have: \[ V_{\text{pyramid}} = \frac{1}{3} \times 600 \text{ in}^3 \] \[ V_{\text{pyramid}} = 200 \text{ in}^3 \]
Thus, the volume of the rectangular pyramid is \( \boxed{200} \text{ in}^3 \).