1. **Problem Statement:** Find the volume of a sphere with radius $r = 10.5$ miles. 2. **Formula:** The volume $V$ of a sphere is given by the formula: $$V = \frac{4}{3} \pi r^3$$ 3. **Calculation:** Substitute $r = 10.5$ into the formula: $$V = \frac{4}{3} \pi (10.5)^3$$ Calculate the cube of 10.5: $$10.5^3 = 10.5 \times 10.5 \times 10.5 = 1157.625$$ So, $$V = \frac{4}{3} \pi \times 1157.625$$ 4. Multiply $\frac{4}{3}$ by 1157.625: $$\frac{4}{3} \times 1157.625 = \frac{4 \times 1157.625}{3} = \frac{4630.5}{3}$$ Show cancellation: $$\frac{\cancel{4} \times 1157.625}{\cancel{3}} = 1543.5$$ 5. Now multiply by $\pi$ (approximate $\pi \approx 3.1416$): $$V \approx 1543.5 \times 3.1416 = 4849.05$$ 6. **Final Answer:** The volume of the sphere is approximately **4849.05 cubic miles**. This corresponds to option A.