Answer
the shuttle travels $1400\pi\,miles$ (exact value) or $4.40\times10^{3}\,miles$ (approximate value)
Work Step by Step
Radius $r=(4000+200)\,miles=4200\,miles$
Inorder to complete $360^{\circ}$ the space shuttle needs 6 hours.
Therefore in 1 hour it covers an angle of $360^{\circ}\times\frac{1}{6}=60^{\circ}$.
That is, central angle $\theta=(60\times\frac{\pi}{180})\,radians=\frac{\pi}{3}\,rad$
Arc length $s=r\times\theta=4200\,miles\times\frac{\pi}{3}=1400\pi\,miles=4400\,miles$
