1. **State the problem:** We want to find the total length $L$ of the string in a ball of string with radius $r = 2$ m. 2. **Formula and assumptions:** The ball is roughly a sphere, so its volume $V$ is given by the formula $$V = \frac{4}{3} \pi r^3.$$ The string is packed inside this volume. If the string has a uniform circular cross-section with radius $r_s$, then the volume of the string is also $$V = L \times A,$$ where $A = \pi r_s^2$ is the cross-sectional area of the string. 3. **Important rule:** To find $L$, we rearrange the volume formula: $$L = \frac{V}{A} = \frac{\frac{4}{3} \pi r^3}{\pi r_s^2} = \frac{4}{3} \frac{r^3}{r_s^2}.$$ 4. **Estimate string radius:** Typical string radius $r_s$ is about 1 mm = 0.001 m. 5. **Calculate volume of the ball:** $$V = \frac{4}{3} \pi (2)^3 = \frac{4}{3} \pi 8 = \frac{32}{3} \pi \approx 33.51 \text{ m}^3.$$ 6. **Calculate length $L$:** $$L = \frac{4}{3} \frac{(2)^3}{(0.001)^2} = \frac{4}{3} \frac{8}{0.000001} = \frac{32}{3} \times 10^6 \approx 10.7 \times 10^6 = 1.07 \times 10^7 \text{ meters}.$$ 7. **Answer:** To the nearest order of magnitude, the total length $L$ of the string is about $$10^7$$ meters, or 10 million meters.