To find the volume of a similar rectangular pyramid when given a scale factor, we can use the property of similar solids. The volume of similar solids scales with the cube of the scale factor.
If the original pyramid has a volume \( V \), and the scale factor is \( k = \frac{2}{3} \), then the volume \( V' \) of the new pyramid can be calculated using the formula:
\[ V' = V \cdot k^3 \]
Now, calculating \( k^3 \) for the scale factor \( k = \frac{2}{3} \):
\[ k^3 = \left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3} = \frac{8}{27} \]
Therefore, the volume of the new pyramid is:
\[ V' = V \cdot \frac{8}{27} \]
To find the volume of the new pyramid, you would need to multiply the original volume \( V \) of the pyramid by \( \frac{8}{27} \). If you know the original volume, substitute that value into the equation above to find the new volume \( V' \).
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