1. **State the problem:** We have a cylinder-shaped candy container with volume $125.6$ cubic centimeters and height $10$ centimeters. We need to find the radius $r$ of the container. 2. **Formula used:** The volume $V$ of a cylinder is given by the formula: $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute known values:** Given $V = 125.6$, $h = 10$, and using $\pi \approx 3.14$, substitute into the formula: $$125.6 = 3.14 \times r^2 \times 10$$ 4. **Isolate $r^2$:** Divide both sides by $3.14 \times 10$: $$r^2 = \frac{125.6}{3.14 \times 10}$$ Show cancellation: $$r^2 = \frac{125.6}{\cancel{3.14} \times \cancel{10}}$$ Calculate denominator: $$r^2 = \frac{125.6}{31.4}$$ 5. **Calculate $r^2$:** $$r^2 = 4$$ 6. **Find $r$ by taking the square root:** $$r = \sqrt{4} = 2$$ **Final answer:** The radius of the container is $2$ centimeters.