1. **State the problem:** We need to find the height $h$ of a cylinder given its volume $V = 668.6944$ m³ and radius $r = 4.4$ m. 2. **Formula used:** The volume of a cylinder is given by $$V = \pi r^2 h$$ where $\pi \approx 3.14$, $r$ is the radius, and $h$ is the height. 3. **Rearrange the formula to solve for height $h$:** $$h = \frac{V}{\pi r^2}$$ 4. **Substitute the known values:** $$h = \frac{668.6944}{3.14 \times (4.4)^2}$$ 5. **Calculate the denominator:** $$3.14 \times (4.4)^2 = 3.14 \times 19.36 = 60.7504$$ 6. **Calculate the height:** $$h = \frac{668.6944}{60.7504}$$ 7. **Simplify the fraction:** $$h = \frac{\cancel{668.6944}}{\cancel{60.7504}} = 11$$ 8. **Final answer:** The approximate height of the cylinder is **11 meters**.