Question

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

$1:4$

$1:2$

$1:1$

$2:1$

$4:1$

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Written solution:

Felicia's diameter is twice as much as Alex's which means that her radius is also twice as much.

Recall that the formula for the area of a circle is $\pi r^2.$ If the radius is doubled, then the area is quadrupled.

This means that the base of Felicia's can has $4$ times the area as the base of Alex's can.

We also see that Alex's can is twice as tall as Felicia's can. The formula for the volume of a can is base times height.

Using this formula, we see that Felicia's can will have twice the volume of Alex's can since $4 \div 2 = 2.$

Thus, the correct answer is B.

2019 AMC 8 Problem 9

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Problem 9 in Other Years