[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=475.17\\ h=15 \end{cases}\implies 475.17=\cfrac{\pi r^2(15)}{3}\implies 475.17=5\pi r^2 \\\\\\ \cfrac{475.17}{5\pi }=r^2\implies \sqrt{\cfrac{475.17}{5\pi }}=r\implies 5.5\approx r~\hfill \underset{diameter}{\stackrel{2(5.5)}{\approx 11}}[/tex]
