2012-II-16

答案：B
設 $\angle AOB=\theta$。

考慮扇形 $OAB$，可得

$\begin{array}{rcl}
2\pi (30) \times \dfrac{\theta}{360^\circ} & = & 12 \pi \\
\theta & = & 72^\circ
\end{array}$

考慮扇形 $OCD$，可得

$\begin{array}{rcl}
2\pi (30+AC)\times \dfrac{72^\circ}{360^\circ} & = & 16 \pi \\
30 + AC & = & 40 \\
AC & = & 10 \mbox{ cm}
\end{array}$