2004 AMC 12A Problems/Problem 9: Difference between revisions
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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 | <math> \mathrm{(A) \ } 10 \qquad \mathrm{(B) \ } 25 \qquad \mathrm{(C) \ } 36 \qquad \mathrm{(D) \ } 50 \qquad \mathrm{(E) \ } 60 </math> | ||
==Solution== | ==Solution== | ||
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*[[2004 AMC 10A Problems/Problem 12|Next Problem]] | *[[2004 AMC 10A Problems/Problem 12|Next Problem]] | ||
[[Category:Introductory Algebra Problems]] | |||
Revision as of 11:09, 5 November 2006
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 , is 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 
.
