Question

What is the lateral and surface area of a cone with a radius of 3 and height of 3​

Answer 1

`\bf \textit{lateral area of a cone}\\\\ LA=\pi r√(r^2+h^2)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=3 \end{cases}\implies LA=\pi (3)√(3^2+3^2) \\\\\\ LA=3\pi √(2(3^2))\implies \boxed{LA=9\pi √(2)} \\\\[-0.35em] ~\dotfill`

`\bf \textit{total surface area of a cone}\\\\ SA=\pi r√(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 √(2)}+\pi 3^2 \\\\\\ SA=9\pi √(2)+9\pi \implies SA\approx 68.26`