1. **State the problem:** We are given the volume of a sphere as $36000\pi$ units³ and need to find its radius. 2. **Formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ where $V$ is the volume and $r$ is the radius. 3. **Substitute the given volume into the formula:** $$36000\pi = \frac{4}{3} \pi r^3$$ 4. **Divide both sides by $\pi$ to simplify:** $$\cancel{\pi} 36000 = \frac{4}{3} \cancel{\pi} r^3 \implies 36000 = \frac{4}{3} r^3$$ 5. **Multiply both sides by $\frac{3}{4}$ to isolate $r^3$:** $$r^3 = 36000 \times \frac{3}{4} = 36000 \times 0.75 = 27000$$ 6. **Find the cube root of both sides to solve for $r$:** $$r = \sqrt[3]{27000}$$ 7. **Calculate the cube root:** Since $30^3 = 27000$, we have $$r = 30$$ **Final answer:** The radius of the sphere is $30$ units.