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Relation Between Two Right Cylinders

Source: 2015 AMC 12A #7/10A #9

February 4, 2015
ratioAMC

Problem Statement

Two right circular cylinders have the same volume. The radius of the second cylinder is 10%10\% more than the radius of the first. What is the relationship between the heights of the two cylinders?
<spanclass=′latex−bold′>(A)</span>The second height is 10% less than the first.<span class='latex-bold'>(A) </span>\text{The second height is 10\% less than the first.}
<spanclass=′latex−bold′>(B)</span>The first height is 10% more than the second.<span class='latex-bold'>(B) </span>\text{The first height is 10\% more than the second.}
<spanclass=′latex−bold′>(C)</span>The second height is 21% less than the first.<span class='latex-bold'>(C) </span>\text{The second height is 21\% less than the first.}
<spanclass=′latex−bold′>(D)</span>The first height is 21% more than the second.<span class='latex-bold'>(D) </span>\text{The first height is 21\% more than the second.}
<spanclass=′latex−bold′>(E)</span>The second height is 80% of the first.<span class='latex-bold'>(E) </span>\text{The second height is 80\% of the first.}
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