A rectangular prism has a volume of 252in.3. if the rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?

Answer 1

To find the volume of the rectangular pyramid, we need to use the formula for the volume of a pyramid, which is:

\(V = \frac{1}{3} \times \text{base area} \times \text{height}\).

Since the base and height of the rectangular pyramid are congruent to the prism, the dimensions of the base are the same as the base of the prism, and the height of the pyramid is the same as the height of the prism.

Let's assume the dimensions of the rectangular prism are length = \(l\), width = \(w\), and height = \(h\).

Given that the volume of the prism is 252 in^3, we have:

\(V_{\text{prism}} = l \times w \times h = 252\)

Since the base and height of the pyramid are the same as the prism, the base area is:

\(\text{Base area} = l \times w\).

Plugging this into the formula for the volume of the pyramid, we get:

\(V_{\text{pyramid}} = \frac{1}{3} \times l \times w \times h = \frac{1}{3} \times V_{\text{prism}} = \frac{1}{3} \times 252 = 84\) in^3.

Therefore, the volume of the rectangular pyramid is 84 in^3.