The slant height is the hypotenuse of the right triangle which legs are the radius of the cone and the height. Then we have:
[tex]\begin{gathered} c^2=6^2+2^2 \\ c^2=36+4 \\ c^2=40 \\ c=\sqrt[]{40} \end{gathered}[/tex]Therefore the slant height of the cone is the square root of 40. This is approximately 6.32.