1. **State the problem:** We need to find the volume of a regulation men's basketball given its diameter is approximately 9.55 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: $$r = \frac{9.55}{2} = 4.775$$ inches. 4. **Substitute values into the formula:** $$V = \frac{4}{3} \times 3.14 \times (4.775)^3$$ 5. **Calculate the cube of the radius:** $$4.775^3 = 4.775 \times 4.775 \times 4.775 = 108.865$$ (rounded to three decimal places) 6. **Calculate the volume:** $$V = \frac{4}{3} \times 3.14 \times 108.865$$ 7. **Multiply constants:** $$\frac{4}{3} \times 3.14 = \frac{4 \times 3.14}{3} = \frac{12.56}{3} = 4.1867$$ (rounded to four decimal places) 8. **Final volume calculation:** $$V = 4.1867 \times 108.865 = 455.6$$ cubic inches (rounded to the nearest tenth). **Answer:** $$V = 455.6 \text{ in}^3$$