[tex]\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}~~
\begin{cases}
r=radius\\
-----\\
V=972\pi
\end{cases}\implies 972\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3\cdot 972\pi }{4\pi }=r^3
\\\\\\
729=r^3\implies \sqrt[3]{729}=r\implies \boxed{9=r}[/tex]
now, recall that a diameter is twice as long as the radius, so the diameter is 2r.
