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1991 AMC 12 Question 8

AMC12 · 1991 AMC 12

Question 8

Liquid $X$ does not mix with water. Unless obstructed, it spreads out on the surface of water to form a circular film $0.1$ cm thick. A rectangular box measuring $6$ cm by $3$ cm by $12$ cm is filled with liquid $X.$ Its contents are poured onto a large body of water. What will be the radius, in centimeters, of the resulting circular film?
  1. $\frac{\sqrt{216}}{\pi}$
  2. $\sqrt{\frac{216}{\pi}}$
  3. $\sqrt{\frac{2160}{\pi}}$
  4. $\frac{216}{\pi}$
  5. $\frac{2160}{\pi}$