[tex]\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}~~
\begin{cases}
r=radius\\
-----\\
V=128
\end{cases}\implies 128=\cfrac{4\pi r^3}{3}\implies 128(3)=4\pi r^3[/tex]
[tex]\bf \cfrac{128(3)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{128(3)}{4\pi }}=r^3\implies \sqrt[3]{\cfrac{96}{\pi }}=r\implies \sqrt[3]{\cfrac{8\cdot 12}{\pi }}=r
\\\\\\
\sqrt[3]{\cfrac{2^3\cdot 12}{\pi }}=r\implies 2\sqrt[3]{\cfrac{12}{\pi }}=r\\\\
-------------------------------\\\\
\textit{and since the diameter is \underline{twice as the radius}}\qquad d=4\sqrt[3]{\cfrac{12}{\pi }}[/tex]
