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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 one year ago one year ago

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1. Jonask

$\huge{V(R)=\frac{ 4 }{ 3 }\pi R^3+\frac{\pi l}{2} R^3+2SR}$