1. **State the problem:** We need to find the volume of a sphere with radius $r = 4.5$ feet. 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:** $$V = \frac{4}{3} \pi (4.5)^3$$ 4. **Calculate the cube of the radius:** $$4.5^3 = 4.5 \times 4.5 \times 4.5 = 91.125$$ 5. **Plug this value back into the volume formula:** $$V = \frac{4}{3} \pi \times 91.125$$ 6. **Multiply the constants:** $$V = \frac{4}{3} \times 91.125 \times \pi = \frac{4 \times 91.125}{3} \pi$$ 7. **Simplify the fraction:** $$\frac{4 \times 91.125}{3} = \frac{364.5}{3} = 121.5$$ 8. **So the volume is:** $$V = 121.5 \pi$$ 9. **Use the approximate value of $\pi \approx 3.1416$ to find a decimal value:** $$V \approx 121.5 \times 3.1416 = 381.7$$ 10. **Final answer:** The volume of the sphere is approximately **381.7 cubic feet** when rounded to the nearest tenth.