1. **State the problem:** Find the radius of a cylinder with volume $V = 5070\pi$ cubic centimeters and height $h = 30$ centimeters. 2. **Formula for the volume of a cylinder:** $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute the known values:** $$5070\pi = \pi r^2 \times 30$$ 4. **Divide both sides by $\pi$ to simplify:** $$5070 = r^2 \times 30$$ 5. **Divide both sides by 30 to isolate $r^2$:** $$\frac{5070}{\cancel{30}} = r^2 \times \cancel{30}$$ $$169 = r^2$$ 6. **Take the square root of both sides to find $r$:** $$r = \sqrt{169} = 13$$ **Final answer:** The radius of the cylinder is $13$ centimeters.