1. **State the problem:** We need to find the radius $r$ of a cone given its volume $V = 150.72$ cubic millimeters and height $h = 9$ millimeters. 2. **Formula:** The volume of a cone is given by $$V = \frac{1}{3} \pi r^2 h$$ where $V$ is volume, $r$ is radius, and $h$ is height. 3. **Substitute known values:** $$150.72 = \frac{1}{3} \pi r^2 \times 9$$ 4. **Simplify the right side:** $$150.72 = 3 \pi r^2$$ 5. **Isolate $r^2$ by dividing both sides by $3\pi$:** $$r^2 = \frac{150.72}{3\pi}$$ 6. **Show cancellation explicitly:** $$r^2 = \frac{150.72}{\cancel{3}\pi} \times \frac{\cancel{1}}{\cancel{3}} = \frac{150.72}{3\pi}$$ 7. **Calculate the value:** $$r^2 = \frac{150.72}{3 \times 3.1416} = \frac{150.72}{9.4248} \approx 16$$ 8. **Take the square root to find $r$:** $$r = \sqrt{16} = 4$$ 9. **Answer:** The radius of the cone is approximately **4 millimeters**. This is rounded to the nearest whole number as requested.