Answer:
[tex]\large\boxed{R=r\sqrt3}[/tex]
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2h[/tex]
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi R^2h[/tex]
The volume of a cone is equal the volume of a cylinder.
Therefore we have the equation:
[tex]\dfrac{1}{3}\pi R^2h=\pi r^2h[/tex] divide both sides by πh
[tex]\dfrac{1}{3}R^2=r^2[/tex] multiply both sides by 3
[tex]R^2=3r^2\to R=\sqrt{3r^2}\\\\R=r\sqrt3[/tex]
