[tex]\textit{volume of a hemisphere}\\ V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{2}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=486\pi \end{cases}\implies 486\pi =\cfrac{4\pi r^3}{6} \implies 6(486\pi )=4\pi r^3 \\\\\\ \cfrac{6(486\pi )}{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies \boxed{9=r} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{surface area of a hemisphere}\\\\ SA=4\pi r^2\cdot \cfrac{1}{2}\implies \stackrel{\textit{we know that r = 9}}{SA=2\pi (9)^2}\implies SA=162\pi \implies SA\approx 508.94[/tex]
