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)
Responses

300 in.3
300 in. cubed

200 in.3
200 in. cubed

1,800 in.3
1,800 in. cubed

1,200 in.3

1 answer

The volume \( V \) of a rectangular prism is given by the formula:

\[ V = \text{length} \times \text{width} \times \text{height} \]

The volume \( V \) of a rectangular pyramid with the same base and height as the prism is given by:

\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]

Since the base area of the rectangular pyramid is the same as that of the prism, we can say:

\[ \text{base area} = \text{length} \times \text{width} \]

Thus, the volume of the pyramid can be expressed as:

\[ V = \frac{1}{3} \times \text{length} \times \text{width} \times \text{height} = \frac{1}{3} \times \text{Volume of the prism} \]

Given that the volume of the rectangular prism is 600 in³, the volume of the rectangular pyramid is:

\[ V = \frac{1}{3} \times 600 = 200 , \text{in.}^3 \]

Therefore, the answer is:

200 in.³ or 200 in. cubed.