2019 AMC 8 Problem 9
Attempt Problem 9 of the 2019 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are cm in diameter and cm high. Felicia buys cat food in cylindrical cans that are cm in diameter and cm high. What is the ratio of the volume of one of Alex’s cans to the volume of one of Felicia’s cans?
Small hint:
Volume is
Big hint:
Felicia’s radius doubles while her height halves
Video solution:
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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 If the radius is doubled, then the area is quadrupled.
This means that the base of Felicia’s can has 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
Thus, the correct answer is B.
Problem 9 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
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