Tuesday, June 2, 2020

06/02/2020 (2019: AMC 8, Problem 9)

Q: 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?

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

The volume of a can is ((1/2 of the diameter)^2)(height)(pi).

That means that the volume of Alex's can is (3^2)(12)(pi) = 108pi.

That also means that the volume of Felicia's can is (6^2)(6)(pi) = 216pi.

108pi : 216pi = 108 : 216 = 18 : 36 = 1 : 2, making the answer B.

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