1. **State the problem:** We are given a cylinder with volume $V = 62.8$ cubic inches and radius $r = 2$ inches. We need to find the height $h$ of the cylinder. 2. **Formula:** The volume of a cylinder is given by the formula: $$V = \pi r^2 h$$ where $V$ is volume, $r$ is radius, and $h$ is height. 3. **Substitute known values:** $$62.8 = \pi \times 2^2 \times h$$ 4. **Simplify:** $$62.8 = \pi \times 4 \times h$$ 5. **Isolate $h$:** $$h = \frac{62.8}{4\pi}$$ 6. **Show cancellation:** $$h = \frac{62.8}{\cancel{4}\pi} \times \frac{\cancel{1}}{1}$$ 7. **Calculate $h$ numerically:** Using $\pi \approx 3.14$, $$h = \frac{62.8}{4 \times 3.14} = \frac{62.8}{12.56} = 5$$ 8. **Conclusion:** The height of the cylinder is approximately 5 inches. **Final answer:** 5 in.