2019 AMC 8

Complete problem set with solutions and individual problem pages

Problem 9 Easy

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?

  • A.

    1:4

  • B.

    1:2

  • C.

    1:1

  • D.

    2:1

  • E.

    4:1

Answer:B

Solution 1

Using the formula for the volume of a cylinder, we get Alex, 108\pi, and Felicia, 216\pi. 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{\textbf{(B)}\ 1:2} as the answer.

 

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}.

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