[tex]\bf \textit{lateral surface area of a cone}\\\\
LA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}~~
\begin{cases}
r=radius\\
h=height\\
-------\\
r=11\\
\stackrel{slant~height}{\sqrt{r^2+h^2}}=24
\end{cases}\implies LA=\pi (11)(24)
\\\\\\
\boxed{LA=264\pi }\\\\
-------------------------------[/tex]
[tex]\bf \textit{total surface area of a cone}\\\\
SA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}+\pi r^2~~
\begin{cases}
r=radius\\
h=height\\
-------\\
r=11\\
\stackrel{slant~height}{\sqrt{r^2+h^2}}=24
\end{cases}
\\\\\\
SA=\pi (11)(24)+\pi (11)^2\implies SA=264\pi +121\pi
\\\\\\
\boxed{SA=385\pi }[/tex]
