Question

Find the surface area of the cone in terms of pie.

Answer 1

Check the picture below.

$\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} ~\hfill r&=radius\\ ~\hfill h&=height\\ \sqrt{r^2+h^2}&=slant~height\\[-0.5em] \hrulefill&\hrulefill\\ ~\hfill r&=6\\ \sqrt{r^2+h^2}&=18 \end{cases} \\\\\\ SA=\pi (6)(18)+\pi (6)^2\implies SA=108\pi +36\pi \implies SA=144\pi$