To find the volume of a rectangular pyramid whose base and height are congruent to a rectangular prism, we can use the formulas for the volumes of both shapes.
The volume \( V \) of a rectangular prism is calculated using the formula: \[ V = \text{length} \times \text{width} \times \text{height} \] For a given volume of 600 in\(^3\) for the prism, we have: \[ V_{prism} = 600 \text{ in}^3 \]
The volume \( V \) of a rectangular pyramid is given by the formula: \[ V = \frac{1}{3} \times \text{base area} \times \text{height} \] Since the base of the pyramid is congruent to the base of the prism and the height of the pyramid is the same as the height of the prism, we can express the volume of the pyramid as: \[ V_{pyramid} = \frac{1}{3} \times \text{base area} \times \text{height} = \frac{1}{3} \times ( \text{length} \times \text{width} ) \times \text{height} \]
Since the base area and height are the same as the prism, we can say: \[ V_{pyramid} = \frac{1}{3} \times V_{prism} \] Substituting the known volume of the prism: \[ V_{pyramid} = \frac{1}{3} \times 600 \text{ in}^3 = 200 \text{ in}^3 \]
Thus, the volume of the rectangular pyramid is 200 in.³.
So, the correct response is: 200 in.³.