1. **State the problem:** We need to find the volume of a sphere with a diameter of 72 cm. 2. **Formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius of the sphere. 3. **Find the radius:** The radius is half the diameter: $$r = \frac{72}{2} = 36 \text{ cm}$$ 4. **Calculate the volume:** $$V = \frac{4}{3} \pi (36)^3$$ 5. **Calculate $36^3$:** $$36^3 = 36 \times 36 \times 36 = 46656$$ 6. **Substitute and simplify:** $$V = \frac{4}{3} \pi \times 46656$$ 7. **Multiply numerator:** $$4 \times 46656 = 186624$$ 8. **Write volume as:** $$V = \frac{186624}{3} \pi$$ 9. **Simplify fraction:** $$\frac{186624}{3} = \cancel{\frac{186624}{3}} = 62208$$ 10. **Final volume expression:** $$V = 62208 \pi$$ 11. **Approximate using $\pi \approx 3.1416$:** $$V \approx 62208 \times 3.1416 = 195432.19 \text{ cubic centimeters}$$ **Answer:** C 195,432.19 cubic centimeters