1. **State the problem:** We are given the volume $V = 150.72$ cubic millimeters and height $h = 9$ millimeters of a cone, and we need to find its radius $r$ rounded to the nearest whole number. 2. **Formula for the volume of a cone:** $$V = \frac{1}{3} \pi r^2 h$$ This formula relates the volume $V$, radius $r$, and height $h$ of a cone. 3. **Substitute the known values:** $$150.72 = \frac{1}{3} \pi r^2 \times 9$$ 4. **Simplify the equation:** $$150.72 = 3 \pi r^2$$ 5. **Isolate $r^2$:** $$r^2 = \frac{150.72}{3 \pi}$$ 6. **Calculate the value inside the fraction:** $$r^2 = \frac{150.72}{3 \times 3.1416} = \frac{150.72}{9.4248}$$ 7. **Simplify the fraction:** $$r^2 = 16$$ 8. **Take the square root of both sides:** $$r = \sqrt{16} = 4$$ 9. **Final answer:** The radius of the cone is approximately **4 millimeters**.