2019 AMC 8 Problems/Problem 9

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 one of Alex's cans to the volume one of Felicia's cans?

$\textbf{(A) }1:4\qquad\textbf{(B) }1:2\qquad\textbf{(C) }1:1\qquad\textbf{(D) }2:1\qquad\textbf{(E) }4:1$

Solution 1

Using the formula for the volume of a cylinder, we get Alex, $\pi108$ , and Felicia, $\pi216$ . We can quickly notice that $\pi$ cancels out on both sides, and that Alex's volume is $1/2$ of Felicia's leaving $1/2 = \boxed{1:2}$ as the answer.

~aopsav

Solution 2

Using the formula for the volume of a cylinder, we get that the volume of Alex's can is $3^2\cdot12\cdot\pi$ , and that the volume of Felicia's can is $6^2\cdot6\cdot\pi$ . Now we divide the volume of Alex's can by the volume of Felicia's can, so we get $\frac{1}{2}$ , which is $\boxed{\textbf{(B)}\ 1:2}$ ~~SmileKat32

Solution 3

The ratio of the numbers is $1/2$ . 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 $1(2)/2(2)$ = \boxed{\textbf{(B)}\ 1:2}$

-Lcz

2019 AMC 8 (Problems • Answer Key • Resources)
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2019 AMC 8 Problems/Problem 9

Contents

Solution 1

Solution 2

Solution 3

See Also