[tex]\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\quad
\begin{cases}
r=radius\\
------\\
r=4
\end{cases}\implies V=\cfrac{4\pi 4^3}{3}\implies V=\cfrac{256\pi }{3}\\\\
-------------------------------\\\\
\cfrac{sphere}{cylinder}\qquad \cfrac{2}{3}\impliedby ratio~thus\implies \cfrac{2}{3}=\cfrac{\stackrel{sphere}{v}}{\stackrel{cylinder}{v}}
\implies
\cfrac{2}{3}=\cfrac{\frac{256\pi }{3}}{v}
\\\\\\
v=\cfrac{3\cdot \frac{256\pi }{3}}{2}\implies v=\cfrac{256\pi }{2}\implies v=128\pi [/tex]
