# 1991 AHSME Problems/Problem 8

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## Problem

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? $\text{(A)} \frac{\sqrt{216}}{\pi} \quad \text{(B)} \sqrt{\frac{216}{\pi}} \quad \text{(C)} \sqrt{\frac{2160}{\pi}} \quad \text{(D)} \frac{216}{\pi} \quad \text{(E)} \frac{2160}{\pi}$

## Solution $\fbox{C}$ The volume of liquid $X$ is $6 \times 3 \times 12 = 216$, so if the radius is $r$, then using the formula for the volume of a cylinder, we get $\pi r^2 \times 0.1 = 216 \implies \pi r^2 = 2160 \implies r = \sqrt{\frac{2160}{\pi}}.$

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