1. **State the problem:** We need to find the volume of a sphere with a diameter of 16 inches. 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, so $$r = \frac{16}{2} = 8 \text{ inches}$$ 4. **Calculate the volume:** Substitute $r = 8$ into the volume formula: $$V = \frac{4}{3} \pi (8)^3 = \frac{4}{3} \pi 512$$ 5. **Simplify the expression:** $$V = \frac{4}{3} \times 512 \times \pi = \frac{4 \times 512}{3} \pi = \frac{2048}{3} \pi$$ 6. **Evaluate the numerical value:** Using $\pi \approx 3.1416$, $$V \approx \frac{2048}{3} \times 3.1416 = 682.6667 \times 3.1416 \approx 2144.66$$ 7. **Final answer:** The volume of the sphere is approximately $$\boxed{2144.66}$$ cubic inches, rounded to the nearest hundredth.