$24 \cdot 9$ liquid $X$ is insoluble in water; when poured into water, it will form a circular film on the water surface with a thickness of $0.1 \mathrm{~cm}$ unless stirred. A rectangular container with length, width, and height of $6 \mathrm{~cm}$, $3 \mathrm{~cm}$, $12 \mathrm{~cm}$ is filled with liquid $X$. When this liquid is poured onto a large water surface, the radius of the circular film formed is
(A) $\frac{\sqrt{216}}{\pi}$.
(B) $\sqrt{\frac{216}{\pi}}$.
(C) $\sqrt{\frac{2160}{\pi}}$.
(D) $\frac{216}{\pi}$.
(E) $\frac{2160}{\pi}$.
(42nd American High School Mathematics Examination, 1991)
［Solution］Let the radius of the circular film be $r$. According to the problem, we have
$$
0.1 \cdot \pi r^{2}=6 \cdot 3 \cdot 12 \text {. }
$$

Thus, $r^{2}=\frac{2160}{\pi}$,
which gives $r=\sqrt{\frac{2160}{\pi}}$. Therefore, the answer is $(C)$.