2015 AMC 10A Problem 9

Two right circular cylinders have the same volume. The radius of the second cylinder is 10\% more than the radius of the first. What is the relationship between the heights of the two cylinders?

\textbf{(A)}\ \text{The second height is } 10\% \text{ less than the first.} \textbf{(B)}\ \text{The first height is } 10\% \text{ more than the second.} \textbf{(C)}\ \text{The second height is } 21\% \text{ less than the first.} \textbf{(D)}\ \text{The first height is } 21\% \text{ more than the second.} \textbf{(E)}\ \text{The second height is } 80\% \text{ of the first.}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.