Question

suppose a similar rectangular pyramid to the one shown has a scale factor of \frac{2}{3}. what would be the volume of the new pyramid? (1 point) 3,285.23 ft.^3 2,190.22 ft.^3 1,400.15 ft.^3 182.52 ft.^3

Explanation:

Step1: Calculate the volume of the original pyramid

The volume formula for a rectangular pyramid is \(V=\frac{1}{3}lwh\). Here, \(l = 24\), \(w=22\), \(h = 28\).

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Step2: Use the scale - factor property for similar solids

If the scale factor of two similar solids is \(k\), the ratio of their volumes is \(k^{3}\). Here, \(k=\frac{2}{3}\).
The volume of the new pyramid \(V_{new}=V_{original}\times k^{3}\)

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Answer:

\(1,460.15\ \text{ft}^3\) (the third option)