A rectangular pyramid has a volume of 480 in.3

Question

. If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism?(1 point)
in.3

Answer 1

The volume of a rectangular pyramid is calculated using the formula:

$$V=\frac{1}{3}\times \text{Base Area}\times \text{Height}$$

Given that the volume of the pyramid is $480,{\text{in}}^3$, we can relate it to the rectangular prism.

The volume of a rectangular prism is calculated using the formula:

$$V=\text{Base Area}\times \text{Height}$$

Since the base area and height of the rectangular prism are congruent to those of the rectangular pyramid, the volume of the rectangular prism can be determined as follows:

The volume of the rectangular prism will be three times that of the pyramid, because:

$$V_{\text{prism}}=3\times V_{\text{pyramid}}=3\times 480,{\text{in}}^3=1440,{\text{in}}^3$$

Therefore, the volume of the rectangular prism is $1440,{\text{in}}^3$.