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jmc

geometry intermediate

Problem

A spherical scoop of vanilla ice cream with radius of 2 inches is dropped onto the surface of a dish of hot chocolate sauce. As it melts, the ice cream spreads out uniformly forming a cylindrical region 8 inches in radius. Assuming the density of the ice cream remains constant, how many inches deep is the melted ice cream? Express your answer as a common fraction.
Solution
The ice cream sphere has volume cubic inches. Let the height of the cylindrical region be ; then, the volume of the cylindrical region is . Thus, we have Dividing both sides by yields inches.
Final answer
\frac{1}{6}