1. **State the problem:** We need to find the volume of a sphere with a diameter of 10 meters. 2. **Recall the 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, so $$r = \frac{10}{2} = 5 \text{ meters}$$ 4. **Calculate the volume:** Substitute $r = 5$ into the volume formula: $$V = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi 125$$ 5. **Simplify the expression:** $$V = \frac{500}{3} \pi$$ 6. **Calculate the numerical value:** Using $\pi \approx 3.1416$, $$V \approx \frac{500}{3} \times 3.1416 = 523.598$$ 7. **Round to the nearest hundredth:** $$V \approx 523.60 \text{ cubic meters}$$ **Final answer:** The volume of the sphere is approximately $523.60$ cubic meters.