1991 AHSME Problems/Problem 8

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 $\pi r^2 \times 0.1 = 216 \implies \pi r^2 = 2160 \implies r = \sqrt{\frac{2160}{\pi}}.$

1991 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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1991 AHSME Problems/Problem 8

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