since the diameter of the cone is 18 meters, then the radius has to be half that, or 9 meters,
[tex]\bf \textit{lateral surface area of a cone}\\\\
LA=\pi r\sqrt{r^2+h^2}~~
\begin{cases}
r=radius\\
h=height\\
\sqrt{r^2+h^2}=slant~height\\
-----------\\
r=9\\
\sqrt{r^2+h^2}=15
\end{cases}\implies LA=\pi (9)(15)
\\\\\\
LA=135\pi [/tex]
