1. **State the problem:** Convert a volume of 14 cubic yards ($14 \text{ yd}^3$) to cubic meters ($\text{m}^3$) using the fact that 1 yard is approximately 0.9144 meters. 2. **Recall the conversion factor for lengths:** $$1 \text{ yd} = 0.9144 \text{ m}$$ 3. **Calculate the conversion factor for volume:** Since we are converting cubic yards to cubic meters, we cube the conversion factor for length: $$1 \text{ yd}^3 = (0.9144)^3 \text{ m}^3$$ 4. **Calculate $(0.9144)^3$:** $$0.9144^3 = 0.9144 \times 0.9144 \times 0.9144 = 0.764554857984$$ 5. **Convert 14 cubic yards to cubic meters:** $$14 \times 0.764554857984 = 10.7037680118$$ 6. **Round to the nearest hundredth:** $$10.7037680118 \approx 10.70$$ **Final answer:** $$14 \text{ yd}^3 \approx \boxed{10.70} \text{ m}^3$$