A cork plug is a three-dimensional solid that can stopper a square, triangular, or circular hole. There is an infinite family of such shapes.
The shape with smallest volume has triangular cross sections.
The plug with the largest volume is made using two cuts from the top diameter to the edge, as illustrated above. Such a plug has 
to obtain a square cross section. For a general such a
plug of height 
and radius 
,
the volume of the plug is
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