1. **State the problem:** We need to find the volume of a sphere with radius $r = 7$ meters. 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:** $$V = \frac{4}{3} \pi (7)^3$$ 4. **Calculate the cube of the radius:** $$7^3 = 7 \times 7 \times 7 = 343$$ 5. **Rewrite the volume expression:** $$V = \frac{4}{3} \pi \times 343$$ 6. **Multiply numerator terms:** $$4 \times 343 = 1372$$ 7. **Express volume as:** $$V = \frac{1372}{3} \pi$$ 8. **Show cancellation step:** $$V = \cancel{\frac{1372}{3}} \pi$$ (no common factors to cancel here, so fraction remains as is) 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 meters **Final answer:** The volume of the sphere is approximately **1436.76** cubic meters.