Question

no additional details were added for this assignment.
describe how the volume of a pyramid compares to the volume of a prism with the same base and height.
use the keypad to type your answer and complete the sentences.
to have the same volume as a prism, it would take pyramids with the same base area and height as the prism.
the formula for the volume of a prism, v, in terms of base area b and height h is.
that means the formula for the volume of a pyramid, v,in terms of base area b and height h is

Explanation:

Step1: Recall volume formulas

The volume formula for a prism is \(V = B\times h\) (where \(B\) is the base area and \(h\) is the height). The volume formula for a pyramid is \(V=\frac{1}{3}B\times h\).

Step2: Compare volumes

Let the volume of the prism be \(V_{p}=B\times h\) and the volume of the pyramid be \(V_{y}=\frac{1}{3}B\times h\). If we want \(n\) pyramids to have the same volume as the prism, then \(n\times V_{y}=V_{p}\). Substitute the formulas: \(n\times\frac{1}{3}B\times h=B\times h\). Solving for \(n\), we divide both sides by \(\frac{1}{3}B\times h\), getting \(n = 3\).

Answer:

To have the same volume as a prism, it would take \(3\) pyramids with the same base area and height as the prism. The formula for the volume of a prism, \(V\), in terms of base area \(B\) and height \(h\) is \(V = B\times h\). That means the formula for the volume of a pyramid, \(V\), in terms of base area \(B\) and height \(h\) is \(V=\frac{1}{3}B\times h\)