Question

12. At track practice, there is a cylindrical water cooler full of water. The athletes drink the water from conical paper cups. The water cooler and a paper cup are shown below. 6 in... How many paper cups can be filled completely using all of the water from the full water cooler? A. 36 2 in. B. 108 16 in. C. 144 4 in. D. 216

Answer 1

Let's calculate each volume:

Volume of the water cooler:

`\begin{gathered} V=\pi\cdot r^2\cdot h \\ V=\pi\cdot(6^2)\cdot16=576\pi \end{gathered}`

Volume of the paper cups:

`\begin{gathered} V=(1)/(3)\cdot\pi\cdot r^2\cdot h \\ V=(1)/(3)\cdot\pi\cdot(2^2)\cdot4=(16)/(3)\pi \end{gathered}`

Therefore:

`(576\pi)/((16)/(3)\pi)=108in^3`
`(a)/(b)/(c)/(d)=(a* d)/(b* c)`
`(576\pi)/((16)/(3)\pi)=(576\pi)/(1)/(16\pi)/(3)=(576\pi*3)/(1*16\pi)=(1728\pi)/(16\pi)=108`