The number of cups that can be filled completely will be given by the division between the volume of the cylinder and the volume of the cone
Then, it will be
[tex]\text{cups}\, =\frac{\text{volume cylinder}}{\text{volume cone}}[/tex]
The volume of a cylinder is
[tex]V=\pi hr^2[/tex]
And the volume of the cone is
[tex]V=\frac{\pi r^2h}{3}[/tex]
Then let's put the values and do the division
[tex]\begin{gathered} \text{cups}\, =\frac{\text{volume cylinder}}{\text{volume cone}} \\ \\ \text{cups}\, =\frac{\pi\cdot16\cdot6^2}{\frac{\pi\cdot2^2\cdot4}{3}} \\ \\ \text{cups}\, =\frac{\pi\cdot16\cdot6^2}{1}\cdot\frac{3}{\pi\cdot2^2\cdot4} \\ \\ \text{cups}\, =\frac{\pi\cdot16\cdot6^2\cdot3}{\pi\cdot16} \\ \\ \text{cups}\, =6^2\cdot3 \\ \\ \text{cups}\, =36\cdot3 \\ \\ \text{cups}\, =108 \end{gathered}[/tex]
Therefore we can fill 108 cups completely
