Explanation
We will use the volume formula to find the radius,
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ 334=\frac{4}{3}\pi r^3 \\ \frac{334*3}{4\pi}=r^3 \\ \frac{1002}{4\pi}=r^3 \\ 79.7370\approx r^3 \\ r\approx\sqrt[3]{79.7370} \\ r\approx4.3041cm \end{gathered}[/tex]And if that is the radius, then the diameter must be:
[tex]Diameter=4.3041*2=8.6082\approx8.6\text{ cm}[/tex]Answer
Approximately 8.6 cm