1952 AHSME Problem 1

If the radius of a circle is a rational number, its area is given by a number which is:

\textbf{(A)\ } \text{rational} \qquad \textbf{(B)\ } \text{irrational} \qquad \textbf{(C)\ } \text{integral} \qquad \textbf{(D)\ } \text{a perfect square }\qquad \textbf{(E)\ } \text{none of these}

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