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Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm in diameter and 12 cm high. Felicia buys cat food in cylindrical cans that are 12 cm in diameter and 6 cm high. What is the ratio of the volume of one of Alex\textquotesingle s cans to the volume of one of Felicia\textquotesingle s cans? (2019 AMC 8, 9) 
Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
Solution 1  Using the formula for the volume of a cylinder, we get Alex,~$\pi108$, and Felicia,~$\pi216$. We can quickly notice that~~cancels out on both sides, and that Alex\textquotesingle s volume is~$\dfrac{1}{2}$~~of Felicia\textquotesingle s leaving~$\dfrac{1}{2}=\boxed{1:2}$~as the answer.  Solution 2  Using the formula for the volume of a cylinder, we get that the volume of Alex\textquotesingle s can is~$3^{2}\cdot12\cdot\pi$, and that the volume of Felicia\textquotesingle s can is~$6^{2}\cdot6\cdot\pi$. Now, we divide the volume of Alex\textquotesingle s can by the volume of Felicia\textquotesingle s can, so we get~$\dfrac{1}{2}$, which is$\boxed{\left( B\right)\textbackslash{} 1:2}.$  Solution 3  The ratio of the numbers is~$\dfrac{1}{2}$. Looking closely at the formula~$r^{2}*h*\pi$, we see that the~$r*h*\pi$~will cancel, meaning that the ratio of them will be~$\dfrac{1\left( 2\right)}{2\left( 2\right)}=\boxed{\left( B\right)\textbackslash{} 1:2}$  Solution 4  The second can is 2 size in each of 2 dimensions, and~$\dfrac{1}{2}$~size in 1 dimension.~$\dfrac{2^{2}}{2}=\boxed{\left( B\right)\textbackslash{} 1:2}$ 