The surface area of a right circular cone is computed as follows:
[tex]SA=\pi rs+\pi r^2[/tex]where r is the radius and s is the slant height of the cone.
Substituting with r = 3 mm and s = 4 mm, we get:
[tex]\begin{gathered} SA=\pi\cdot3\cdot4+\pi\cdot3^2 \\ SA=12\pi+9\pi \\ SA=21\pi \\ SA\approx66\text{ mm}^2 \end{gathered}[/tex]