1. **State the problem:** We need to find the volume of a sphere with a diameter of 30 miles. 2. **Formula:** The volume $V$ of a sphere is given by the formula: $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius of the sphere. 3. **Find the radius:** The radius $r$ is half the diameter, so: $$r = \frac{30}{2} = 15 \text{ miles}$$ 4. **Calculate the volume:** Substitute $r = 15$ into the volume formula: $$V = \frac{4}{3} \pi (15)^3 = \frac{4}{3} \pi (3375)$$ 5. **Simplify:** $$V = \frac{4}{3} \times 3375 \times \pi = 4500 \pi$$ 6. **Final answer:** The volume of the sphere is: $$V = 4500 \pi \approx 14137.17 \text{ cubic miles}$$ This means the sphere's volume is approximately 14137.17 cubic miles.