Question

How many paper cups can be filled completely by using all of the water from the water cooler ? A) 36B) 108C)144D) 216

Answer 1

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

`\text{cups}\, =\frac{\text{volume cylinder}}{\text{volume cone}}`

The volume of a cylinder is

`V=\pi hr^2`

And the volume of the cone is

`V=(\pi r^2h)/(3)`

Then let's put the values and do the division

`\begin{gathered} \text{cups}\, =\frac{\text{volume cylinder}}{\text{volume cone}} \\ \\ \text{cups}\, =(\pi\cdot16\cdot6^2)/((\pi\cdot2^2\cdot4)/(3)) \\ \\ \text{cups}\, =(\pi\cdot16\cdot6^2)/(1)\cdot(3)/(\pi\cdot2^2\cdot4) \\ \\ \text{cups}\, =(\pi\cdot16\cdot6^2\cdot3)/(\pi\cdot16) \\ \\ \text{cups}\, =6^2\cdot3 \\ \\ \text{cups}\, =36\cdot3 \\ \\ \text{cups}\, =108 \end{gathered}`

Therefore we can fill 108 cups completely