we know it has a diameter of 8, thus its radius is half that or namely 4.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} h=height\\ r=radius\\[-0.5em] \hrulefill\\ r=4\\ V=464.603 \end{cases}\implies 464.603=\cfrac{\pi (4)^2 h}{3} \\\\\\ 3(464.603)=\pi (4)^2 h\implies \cfrac{3(464.603)}{\pi (4)^2}=h\implies 27.73\approx h[/tex]
