6. (USS) 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 $\mathcal{M}$. Show that the volume $V(R)$ of this set equals
$$V(R)=\frac{4}{3} \pi R^{3}+\frac{\pi}{2} l R^{2}+2 S R$$