from volume to slant height

The volume of a right circular cone is given by: $V=\dfrac{1}{3}\pi r^2 h$

Substituting, we get

$\dfrac{2}{3}\pi=\dfrac{1}{3}\pi r^2h$

After simplifying, we get

$2=r^2h$ , however, $h=2r$ , so,

$2=r^2(2r)$

$2=2r^3$

$1=r^3$

$1=r$

or

$r=1$

It follows that,

$h=2r=2(1)=2$

Finally, the slant height is $\sqrt{2^2+1^2}=\sqrt{4+1}=$ $\color{#D61F06}{\large \boxed{\sqrt{5}}}$