1. **State the problem:** We need to find the radius $r$ of a cone given its volume and height. 2. **Given formula:** The volume $V$ of a cone is given by $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Given values:** $$h = 15$$ $$V = 180\pi$$ 4. **Substitute the known values into the formula:** $$180\pi = \frac{1}{3} \pi r^2 \times 15$$ 5. **Simplify the right side:** $$180\pi = \frac{1}{3} \times 15 \times \pi r^2 = 5\pi r^2$$ 6. **Divide both sides by $\pi$ to cancel it out:** $$\cancel{\pi} 180 = 5 \cancel{\pi} r^2 \implies 180 = 5 r^2$$ 7. **Divide both sides by 5 to isolate $r^2$:** $$\frac{180}{\cancel{5}} = \frac{5 r^2}{\cancel{5}} \implies 36 = r^2$$ 8. **Take the square root of both sides to find $r$:** $$r = \sqrt{36} = 6$$ **Final answer:** The radius of the cone is $6$ cm.