1. **State the problem:** Calculate the volume of a sphere with radius $r=10$ meters. 2. **Formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ 3. **Substitute the radius into the formula:** $$V = \frac{4}{3} \pi (10)^3$$ 4. **Calculate the cube of the radius:** $$10^3 = 1000$$ 5. **Substitute and simplify:** $$V = \frac{4}{3} \pi \times 1000 = \frac{4000}{3} \pi$$ 6. **Approximate using $\pi \approx 3.1416$:** $$V \approx \frac{4000}{3} \times 3.1416 = 1333.333\times 3.1416$$ 7. **Multiply:** $$V \approx 4188.79$$ 8. **Round to the nearest tenth:** $$V \approx 4188.8$$ cubic meters. **Final answer:** The volume of the sphere is approximately **4188.8** cubic meters.