Math CentralQuandaries & Queries


Question from Geli:

A cylinder with a radius r and height 2r+4 contains a cube with edge length r√2. What fraction of cylinder volume is taken up by the cube


The volume of a cylinder of radius $r$ and height $h$ is given by $V = \pi r^2 h \mbox{ cubic units.}$

The volume of a cube of side length $s$ is given by $V = s^{3}$ cubic units.

For your cylinder and cube write the fraction

\[\frac{\mbox{ volume of the cube}}{\mbox{ volume of the cylinder}}\]

and simplify as much as possible.


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