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Jonask
A convex planar polygon \[M\] with perimeter \[l\] and area \[S\] is given. Let M(R) be the set of all points in space that lie a distance at most R from a point of \[M\]. Show that the volume V (R) of this set equals
\[\huge{V(R)=\frac{ 4 }{ 3 }\pi R^3+\frac{\pi l}{2} R^3+2SR}\]