1. **State the problem:** We need to find the volume of a sphere with a diameter of 22 yards. 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. $$r = \frac{22}{2} = 11 \text{ yards}$$ 4. **Calculate the volume:** Substitute $r = 11$ into the volume formula. $$V = \frac{4}{3} \pi (11)^3 = \frac{4}{3} \pi (1331)$$ 5. **Simplify the expression:** $$V = \frac{4}{3} \times 1331 \times \pi = \frac{4 \times 1331}{3} \pi = \frac{5324}{3} \pi$$ 6. **Calculate the numerical value:** $$V \approx \frac{5324}{3} \times 3.1416 = 1774.67 \times 3.1416 \approx 5575.28$$ 7. **Round to the nearest hundredth:** The volume is approximately $5575.28$ cubic yards. **Final answer:** The volume of the sphere is about **5575.28** cubic yards.