Difference between revisions of "2004 AMC 12A Problems/Problem 9"
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{{duplicate|[[2004 AMC 12A Problems|2004 AMC 12A #9]] and [[2004 AMC 10A Problems/Problem 11|2004 AMC 10A #11]]}} | {{duplicate|[[2004 AMC 12A Problems|2004 AMC 12A #9]] and [[2004 AMC 10A Problems/Problem 11|2004 AMC 10A #11]]}} | ||
| − | + | == Problem == | |
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| − | ==Problem== | ||
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the [[diameter]] of the jars is increased by <math>25\%</math> without altering the [[volume]], by what percent must the height be decreased? | A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the [[diameter]] of the jars is increased by <math>25\%</math> without altering the [[volume]], by what percent must the height be decreased? | ||
<math> \mathrm{(A) \ } 10 \qquad \mathrm{(B) \ } 25 \qquad \mathrm{(C) \ } 36 \qquad \mathrm{(D) \ } 50 \qquad \mathrm{(E) \ } 60 </math> | <math> \mathrm{(A) \ } 10 \qquad \mathrm{(B) \ } 25 \qquad \mathrm{(C) \ } 36 \qquad \mathrm{(D) \ } 50 \qquad \mathrm{(E) \ } 60 </math> | ||
| − | ==Solution== | + | == Solution == |
When the diameter is increased by <math>25\%</math>, it is increased by <math>\dfrac{5}{4}</math>, so the area of the base is increased by <math>\left(\dfrac54\right)^2=\dfrac{25}{16}</math>. | When the diameter is increased by <math>25\%</math>, it is increased by <math>\dfrac{5}{4}</math>, so the area of the base is increased by <math>\left(\dfrac54\right)^2=\dfrac{25}{16}</math>. | ||
To keep the volume the same, the height must be <math>\dfrac{1}{\frac{25}{16}}=\dfrac{16}{25}</math> of the original height, which is a <math>36\%</math> reduction. <math>\boxed{\mathrm{(C)}\ 36}</math> | To keep the volume the same, the height must be <math>\dfrac{1}{\frac{25}{16}}=\dfrac{16}{25}</math> of the original height, which is a <math>36\%</math> reduction. <math>\boxed{\mathrm{(C)}\ 36}</math> | ||
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| + | == Video Solution == | ||
| + | https://youtu.be/2A_Fh0Kmu88 | ||
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| + | Education, the Study of Everything | ||
== See also == | == See also == | ||
Latest revision as of 12:37, 8 January 2021
- The following problem is from both the 2004 AMC 12A #9 and 2004 AMC 10A #11, so both problems redirect to this page.
Contents
Problem
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by 
without altering the volume, by what percent must the height be decreased?
Solution
When the diameter is increased by , it is increased by 
, so the area of the base is increased by 
.
To keep the volume the same, the height must be 
of the original height, which is a 
reduction. 
Video Solution
Education, the Study of Everything
See also
| 2004 AMC 12A (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 AMC 12 Problems and Solutions | |
| 2004 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
