1. The problem states: A sphere has a volume of $972\pi$ cm$^3$. We need to find its radius in centimeters. 2. The formula for the volume of a sphere is: $$V = \frac{4}{3} \pi r^3$$ where $V$ is the volume and $r$ is the radius. 3. Substitute the given volume into the formula: $$972\pi = \frac{4}{3} \pi r^3$$ 4. Divide both sides by $\pi$ to simplify: $$972 = \frac{4}{3} r^3$$ 5. Multiply both sides by $\frac{3}{4}$ to isolate $r^3$: $$r^3 = 972 \times \frac{3}{4}$$ 6. Calculate the right side: $$r^3 = 972 \times \frac{3}{4} = 972 \times 0.75 = 729$$ 7. Find the cube root of both sides to solve for $r$: $$r = \sqrt[3]{729}$$ 8. Since $9^3 = 729$, we have: $$r = 9$$ 9. Therefore, the radius of the sphere is 9 cm. Final answer: **9** cm (Option C)