A rectangular pyramid has a volume of 480in.3 if a rectangular prisim has a base and height congruent to the pyramid what is the volume of the prisim

Answer 1

The volume of a rectangular pyramid is given by the formula:

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

Given that the volume of the pyramid is 480 in^3, we can rewrite the formula as:

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

Since the base of the pyramid is a rectangle, the base area is equal to the length times the width. Let's denote the length as L and the width as W.

Now, we are given that the rectangular prism has a base and height congruent to the pyramid. This means that the base area of the prism is the same as the base area of the pyramid, which is L * W.

Therefore, the volume of the prism can be calculated using the formula for the volume of a prism:

Volume = base area * height

Since the base area is L * W and the height is the same as that of the pyramid, we can substitute these values into the formula:

Volume = L * W * height

Now, we know that the volume of the prism is equal to:

Volume = 480 in^3

So, we have:

480 = L * W * height

Since the base area is L * W and the height is 480/3 = 160, the volume of the prism is:

Volume = L * W * 160

Therefore, the volume of the prism is 160LW in^3.