Mathematics, 17.10.2019 21:50 naurelysm
What is the lateral and surface area of a cone with a radius of 3 and height of 3
Answers: 3
![\bf \textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=3 \end{cases}\implies LA=\pi (3)\sqrt{3^2+3^2} \\\\\\ LA=3\pi \sqrt{2(3^2)}\implies \boxed{LA=9\pi \sqrt{2}} \\\\[-0.35em] ~\dotfill](/tpl/images/0329/4783/6104b.png)
![\bf \textit{total surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=3 \end{cases}\implies SA=\boxed{9\pi \sqrt{2}}+\pi 3^2 \\\\\\ SA=9\pi \sqrt{2}+9\pi \implies SA\approx 68.26](/tpl/images/0329/4783/e6e97.png)
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