Question 5
A right circular cone has base radius $r$ and height $h.$ The cone lies on its side on a flat table. As the cone rolls on the surface of the table without slipping, the point where the cone’s base meets the table traces a circular arc centered at the point where the vertex touches the table. The cone first returns to its original position on the table after making $17$ complete rotations. The value of $\frac{h}{r}$ can be written in the form $m\sqrt{n},$ where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. Find $m + n.$