[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} \stackrel{\textit{half of diameter}}{r=6~\hfill }\\ h=7 \end{cases}\implies SA=\pi (6)\sqrt{6^2+7^2}+\pi 6^2 \\\\\\ SA=6\pi \sqrt{85}+36\pi \implies SA=6\pi (\sqrt{85}+6)\implies SA\approx 286.88[/tex]
