1. **State the problem:** We have a circle with radius $R=6400$ km and a central angle $X=22^\circ$. We want to find the length of the arc subtended by this angle. 2. **Formula used:** The length of an arc $s$ in a circle is given by the formula: $$s = R \times \theta$$ where $\theta$ is the central angle in radians. 3. **Convert degrees to radians:** Since $X=22^\circ$, convert to radians using: $$\theta = 22^\circ \times \frac{\pi}{180^\circ} = \frac{22\pi}{180} = \frac{11\pi}{90}$$ 4. **Calculate the arc length:** $$s = 6400 \times \frac{11\pi}{90}$$ 5. **Simplify the expression:** $$s = \frac{6400 \times 11 \pi}{90} = \frac{70400 \pi}{90}$$ 6. **Reduce the fraction:** $$s = \frac{\cancel{70400} \pi}{\cancel{90}} = \frac{70400 \pi}{90}$$ Actually, dividing numerator and denominator by 10: $$s = \frac{7040 \pi}{9}$$ 7. **Approximate the value:** Using $\pi \approx 3.1416$, $$s \approx \frac{7040 \times 3.1416}{9} = \frac{22122.624}{9} \approx 2458.07 \text{ km}$$ **Final answer:** The length of the arc is approximately $2458.07$ km.