AMC 12 2015a Problem 7

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.}