The length (s) of a circular arc is given by
[tex]s=r\cdot\theta[/tex]
where [tex]\theta[/tex] is the central angle in radians
In one hour, the hour hand makes 1/12 of a revolution (2π radians), so travels ...
[tex]s_{h}=(30\,mm) \times \frac{1}{12}\cdot 2\pi=5\pi\,mm[/tex]
In one hour, the minute hand makes 1 full revolution, so travels
[tex]s_{m}=(1.5 \cdot 30\,mm) \times 2\pi = 90\pi\,mm[/tex]
The difference in distance traveled is ...
[tex]s_{m}-s_{h}=(90\pi-5\pi)\,mm=85\pi\,mm \approx 267.0\,mm[/tex]
