1. **State the problem:** We need to find the volume of a sphere with radius $r = 13$ ft. 2. **Formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ This formula calculates the volume inside a sphere given its radius. 3. **Substitute the radius into the formula:** $$V = \frac{4}{3} \pi (13)^3$$ 4. **Calculate the cube of the radius:** $$13^3 = 13 \times 13 \times 13 = 2197$$ 5. **Plug this value back in:** $$V = \frac{4}{3} \pi \times 2197$$ 6. **Multiply numerator terms:** $$4 \times 2197 = 8788$$ 7. **Write the volume as:** $$V = \frac{8788}{3} \pi$$ 8. **Simplify the fraction using cancellation:** $$V = \cancel{\frac{8788}{3}} \pi$$ (no common factors to cancel here, so fraction remains) 9. **Calculate the decimal value:** $$\frac{8788}{3} \approx 2929.33$$ 10. **Multiply by $\pi \approx 3.1416$:** $$V \approx 2929.33 \times 3.1416 = 9201.06$$ 11. **Final answer rounded to nearest hundredth:** $$\boxed{9201.06 \text{ cubic feet}}$$ This is the volume of the sphere with radius 13 ft.