1. **State the problem:** We are given the diameter $D=11.6$ m of a sphere and need to find its volume $V$. 2. **Formula:** The volume of a sphere is given by $$V=\frac{4}{3}\pi r^3$$ where $r$ is the radius of the sphere. 3. **Find the radius:** The radius is half the diameter, $$r=\frac{D}{2}=\frac{11.6}{2}$$ 4. **Simplify radius:** $$r=\cancel{\frac{11.6}{2}}=5.8$$ 5. **Calculate volume:** Substitute $r=5.8$ and $\pi=3.14$ into the volume formula, $$V=\frac{4}{3} \times 3.14 \times (5.8)^3$$ 6. **Calculate $r^3$:** $$5.8^3=5.8 \times 5.8 \times 5.8=195.112$$ 7. **Calculate volume:** $$V=\frac{4}{3} \times 3.14 \times 195.112$$ 8. **Multiply constants:** $$\frac{4}{3} \times 3.14 = \frac{4 \times 3.14}{3} = \frac{12.56}{3} = 4.1867$$ 9. **Final volume:** $$V=4.1867 \times 195.112 = 816.7$$ 10. **Round to nearest tenth:** $$V \approx 816.7 \text{ m}^3$$ **Answer:** The volume of the sphere is approximately $816.7$ cubic meters.