\noindent\textbf{5}

\medskip

In coordinate space, let $S$ be the surface obtained by rotating the line segment $AB$ connecting the point $A(0,\ 0,\ 2)$ and the point $B(1,\ 0,\ 1)$ once around the $z$-axis. Let $P$ be a point on $S$ and $Q$ be a point on the $xy$-plane such that $PQ = 2$. As $P$ and $Q$ move subject to this condition, let $K$ be the region that the midpoint $M$ of the line segment $PQ$ can pass through. Find the volume of $K$.



%% Page 6