9. (1977 9th Canadian Mathematical Olympiad) Given a right circular cone with a base radius of $1 \mathrm{~cm}$ and a slant height of $3 \mathrm{~cm}$, $P$ is a point on the circumference of the base. The shortest path from $P$ around the cone back to $P$ is shown in Figure 313. What is the minimum distance from the vertex $V$ to this path?
9. As shown in the right figure, if the lateral surface of the cone is cut along $V P$ to form a sector, then the shortest path around the cone becomes the chord $P_{1} P_{2}$, and $P_{1} Q P_{2}=2 \pi$, so $2 \theta \cdot 3=2 \pi, \theta=\frac{\pi}{3}$, the required minimum distance $V R=$ $3 \cdot \cos \theta=3 \cdot \cos \frac{\pi}{3}=\frac{3}{2}(\mathrm{~cm})$.