55. Find a sphere that has a volume equal to that of a given cone or cylinder.
55. The volume of a cone is $\frac{\pi}{3} \cdot r^{2} h$; if the radius of the sphere is $R$, then $r^{2} h=4 R^{3}$, and therefore, $R=\sqrt[3]{\frac{r^{2} h}{4}}$.

![](https://cdn.mathpix.com/cropped/2024_05_21_926f0bb262c8f9569516g-084.jpg?height=380&width=511&top_left_y=1912&top_left_x=1184)

Fig. 24.

$6^{*}$

The volume of a cylinder is $\pi r^{2} h$. Therefore, $R_{1}=\sqrt[3]{\frac{3}{4} r^{2} h}$.