1. **State the problem:** We need to find the radius of a cylinder given its height and volume. 2. **Recall the formula for the volume of a cylinder:** $$V = \pi r^2 h$$ where $V$ is volume, $r$ is radius, and $h$ is height. 3. **Given values:** - Volume $V = 4100$ mm$^3$ - Height $h = 19$ mm 4. **Rearrange the formula to solve for radius $r$:** $$r^2 = \frac{V}{\pi h}$$ $$r = \sqrt{\frac{V}{\pi h}}$$ 5. **Substitute the known values:** $$r = \sqrt{\frac{4100}{\pi \times 19}}$$ 6. **Calculate the denominator:** $$\pi \times 19 \approx 3.1416 \times 19 = 59.6904$$ 7. **Calculate the fraction:** $$\frac{4100}{59.6904} \approx 68.68$$ 8. **Calculate the square root:** $$r = \sqrt{68.68} \approx 8.29$$ 9. **Final answer:** The radius of the cylinder is approximately **8.29 mm** to 2 decimal places.