Question

What are the lateral area and the surface of the cone shown below?

Answer 1

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

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