If the slant height of a cone is double its base radius then volume of the cone is

Slant height , $l=2r$

$l=\sqrt{r^2+h^2}$

$2r=\sqrt{r^2+h^2}$

$4r^2=r^2+h^2$

$4r^2-r^2=h^2$

$3r^2=h^2$

$h=\sqrt{3r^2}=r\sqrt{3}$

Volume of cone$=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\pi r^{2}r\sqrt{3}$

$=\frac{1}{3}\pi r^3\sqrt{3}$

$=\frac{1}{3}\pi r^3$