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) $2,190.22 mathrm{ft}^{3}$ $1,460.15 mathrm{ft}^{3}$ $182.52 mathrm{ft}^{3}$ $3,285.33 mathrm{ft}^{3}$

Explanation:

Step1: Calculate the volume of the original pyramid

The formula for the volume of 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 volumes of similar solids

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

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Answer:

\(1460.15\ \text{ft}^3\)