Which shape has the larger volume? How much larger is it?

(1 point)
Responses

The pyramid has a larger volume by three times.
The pyramid has a larger volume by three times.

The prism has a larger volume by three times.
The prism has a larger volume by three times.

The volumes are the same.
The volumes are the same.

The prism has a larger volume by 13
times.

1 answer

To determine which shape has a larger volume and by how much, we need to know the specific dimensions or formulas for calculating the volumes of the pyramid and the prism in question.

However, in general:

  1. The volume of a rectangular prism can be calculated using the formula: \[ V_{\text{prism}} = \text{length} \times \text{width} \times \text{height} \]

  2. The volume of a pyramid with the same base area and height as the prism is: \[ V_{\text{pyramid}} = \frac{1}{3} \times \text{base area} \times \text{height} \]

From these formulas, we see that a pyramid will always have a volume that is one-third the volume of a prism with the same base and height.

Given that there are no specific dimensions provided, we can infer the following:

  • If the base areas and heights are identical, the prism will have a volume three times greater than that of the pyramid.

Therefore, if the choices you provided are correct interpretations based on those calculations, the correct response would be:

The prism has a larger volume by three times.