1. The problem asks for the volume of a sphere with radius $7$ inches. 2. The formula for the volume of a sphere is $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius. 3. Substitute $r = 7$ into the formula: $$V = \frac{4}{3} \pi (7)^3$$ 4. Calculate the cube of $7$: $$7^3 = 7 \times 7 \times 7 = 343$$ 5. So, $$V = \frac{4}{3} \pi \times 343$$ 6. Multiply $4$ and $343$: $$4 \times 343 = 1372$$ 7. Now the volume is: $$V = \frac{1372}{3} \pi$$ 8. Use \cancel to show division simplification: $$V = \cancel{\frac{1372}{3}} \pi$$ (division remains as fraction since 1372 is not divisible by 3 exactly) 9. Calculate the decimal value: $$\frac{1372}{3} \approx 457.3333$$ 10. Multiply by $\pi \approx 3.1416$: $$V \approx 457.3333 \times 3.1416 = 1436.755$$ 11. Round to the nearest hundredth: $$V \approx 1436.76$$ cubic inches. Final answer: The volume of the sphere is approximately $1436.76$ cubic inches.