1. **State the problem:** We need to find the radius of a cylinder given its volume and height. 2. **Formula:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Given values:** $V = 396\pi$ cm³, $h = 11$ cm. 4. **Substitute the known values into the formula:** $$396\pi = \pi r^2 \times 11$$ 5. **Divide both sides by $\pi$ to simplify:** $$\cancel{\pi}396 = \cancel{\pi} r^2 \times 11$$ $$396 = 11 r^2$$ 6. **Divide both sides by 11 to isolate $r^2$:** $$\frac{396}{\cancel{11}} = \frac{11 r^2}{\cancel{11}}$$ $$36 = r^2$$ 7. **Take the square root of both sides to find $r$:** $$r = \sqrt{36} = 6$$ **Final answer:** The radius of the cylinder is $6$ cm.