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Problem of the Day #91: Circular Tubes June 18, 2011

Posted by Albert in : potd , trackback

Circle $O$ has radius $r$ and diameter $d = \overline{AB}$. The circle is curved so that it forms part of the surface of a cylinder and point $A$ touches point $B$. The locus of all lines $\overline{PQ}$ such that points $P$ and $Q$ are on circle $O$ and $\overline{PQ}$ is parallel to $d$ is now drawn in, forming a closed shape. What is the ratio of this shape’s volume to $r^3$?

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