[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=4000\pi \end{cases}\implies 4000\pi =\cfrac{4\pi r^3}{3}\implies 12000\pi =4\pi r^3 \\\\\\ \cfrac{12000\pi }{4\pi }=r^3\implies 3000=r^3\implies \sqrt[3]{3000}=r \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\underline{d}iameter is twice the radius}}{d = 2r}\implies d=2\sqrt[3]{3000}\implies d\approx 28.85[/tex]
