Curved surface area of a cone $$=\pi r l$$
$$=4070\ cm^2$$
Diameter of the cone $$=70\ cm$$
Radius of the cone $$r=\dfrac {70}{2}=35\ cm$$
Let slant height of the cone $$=l$$
From problem $$\pi r l=4070$$
$$\dfrac {22}{7}\times 35\times l=4070\Rightarrow 110\ l=4070$$
$$\Rightarrow l=\dfrac {4070}{110}=37\ cm$$
$$\therefore $$ The slant height of the cone $$=37\ cm$$