2019 AMC 8 Problems/Problem 9
Contents
- 1 Problem 9
- 2 Solution 1
- 3 Solution 2
- 4 Solution 3
- 5 Solution 4
- 6 Solution 5
- 7 Video Solution
- 8 Video Solution by Math-X (Extremely simple approach!!!)
- 9 Video Solution by OmegaLearn
- 10 Video Solution
- 11 Video Solution
- 12 Video Solution
- 13 Video Solution by The Power of Logic(Problem 1 to 25 Full Solution)
- 14 See also
Problem 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?
Solution 1
Using the formula for the volume of a cylinder, we get Alex, , and Felicia, . We can quickly notice that cancels out on both sides and that Alex's volume is of Felicia's leaving 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 , and that the volume of Felicia's can is . Now, we divide the volume of Alex's can by the volume of Felicia's can, so we get , which is .
-(Algebruh123)2020
Solution 3
The ratio of the numbers is . Looking closely at the formula , we see that the will cancel, meaning that the ratio of them will be = .
-Lcz
Solution 4
The second can is size in each of 2 dimensions, and size in 1 dimension. .
~oinava
Solution 5
Without calculating much, you can do ( <-- which is Alex's volume, with ra being Alex's radius diameter), and being her cylinders heightwhich is Felicia's volume, with being Felicia's radius, and being her cylinders height. Since we need the ratio between Alexa's and Felicias, we can do The cancel out, then substitute back in the numbers, which gives you:
-wahahaqueenie
Video Solution
Video Solution by Math-X (Extremely simple approach!!!)
https://youtu.be/IgpayYB48C4?si=wsD8LhZK8hsWd9wu&t=2773
~Math-X
The Learning Royal : https://youtu.be/8njQzoztDGc
Video Solution by OmegaLearn
https://youtu.be/FDgcLW4frg8?t=2440
~ pi_is_3.14
Video Solution
Solution detailing how to solve the problem: https://www.youtube.com/watch?v=G-gEdWP0S9M&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=10
Video Solution
~savannahsolver
Video Solution
~Education, the Study of Everything
Video Solution by The Power of Logic(Problem 1 to 25 Full Solution)
~Hayabusa1
See also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.