Let's calculate each volume:
Volume of the water cooler:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ V=\pi\cdot(6^2)\cdot16=576\pi \end{gathered}[/tex]Volume of the paper cups:
[tex]\begin{gathered} V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h \\ V=\frac{1}{3}\cdot\pi\cdot(2^2)\cdot4=\frac{16}{3}\pi \end{gathered}[/tex]Therefore:
[tex]\frac{576\pi}{\frac{16}{3}\pi}=108in^3[/tex][tex]\frac{a}{b}\div\frac{c}{d}=\frac{a\times d}{b\times c}[/tex][tex]\frac{576\pi}{\frac{16}{3}\pi}=\frac{576\pi}{1}\div\frac{16\pi}{3}=\frac{576\pi\times3}{1\times16\pi}=\frac{1728\pi}{16\pi}=108[/tex]