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?

(A) $\frac{\sqrt{216}}{\pi}$ (B) $\sqrt{\frac{216}{\pi}}$ (C) $\sqrt{\frac{2160}{\pi}}$ (D) $\frac{216}{\pi}$ (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 $\pi r^2 \times 0.1 = 216 \implies \pi r^2 = 2160 \implies r = \sqrt{\frac{2160}{\pi}}.$

See also

1991 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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