Question

how many times greater is the volume of a triangular prism compared to a triangular pyramid with the same base area and height?
o twice
half
o one - third
three times

Explanation:

Step1: Recall the volume formulas

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

Step2: Calculate the ratio

Let's find the ratio \(\frac{V_{prism}}{V_{pyramid}}\). Substitute the formulas: \(\frac{V_{prism}}{V_{pyramid}}=\frac{B\times h}{\frac{1}{3}B\times h}\). The \(B\) and \(h\) terms cancel out (\(B
eq0\), \(h
eq0\)), and we get \(\frac{1}{\frac{1}{3}} = 3\).

Answer:

three times