A right circular cone having radius, \( \mathrm{r} \) is cut by a plane parallel to the base a...

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A right circular cone having radius, \( \mathrm{r} \) is cut by a plane parallel to the base at a height \( \mathrm{h} \) from the base.
The slant height of the frustum is \( \sqrt{h^{2}+\frac{4}{9} r^{2}} \). Show that the volume of the frustum is \( \frac{13}{27} \pi \mathrm{r}^{2} \mathrm{~h} \).
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