[tex]\bf \textit{volume of a right-circular cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=6\\ V=471 \end{cases}\implies 471=\pi r^2(6)\implies \cfrac{471}{6\pi }=r^2 \\\\\\ \sqrt{\cfrac{471}{6\pi }}=r\implies \stackrel{diameter = 2\times radius}{d=2\left( \sqrt{\cfrac{471}{6\pi }} \right)}\implies d\approx 9.997[/tex]
