1991 AMC 12 Problem 8

Question

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?

\frac{\sqrt{216}}{\pi}

\sqrt{\frac{216}{\pi}}

\sqrt{\frac{2160}{\pi}}

\frac{216}{\pi}

\frac{2160}{\pi}

Equate the volume in the box to the volume of the thin circular film

The film volume is

\pi r^2(0.1)

The liquid volume is

6\cdot3\cdot12=216

cubic centimeters. Thus

0.1\pi r^2=216,

so

r^2=\frac{2160}{\pi}

and

r=\sqrt{\frac{2160}{\pi}}.

Thus the correct answer is C.

Problem 8 in other years