A rectangular primary has a volume of 480in³. If a rectangle prism has a base and height congruent to the pyramid, what is the volume of the prism

Answer 1

The volume of a rectangular pyramid can be calculated using the formula:

V = (1/3) * base area * height

Given that the volume of the rectangular pyramid is 480in³, we can set up the equation:

480 = (1/3) * base area * height

Since the base and height of the rectangular prism are congruent to the pyramid, we can equate the base area and height:

base area = base * base = base²
height = base

Plugging this into the equation, we get:

480 = (1/3) * base² * base
480 = (1/3) * base³
1440 = base³
base = ∛1440
base ≈ 11.39 in

Therefore, the volume of the rectangular prism with a base and height congruent to the pyramid is:

V = base² * base
V = 11.39² * 11.39
V ≈ 1463.17 in³

Thus, the volume of the prism is approximately 1463.17in³.