1. The problem asks for the volume of a sphere with radius $r = 4.4$ mm. 2. The formula for the volume of a sphere is $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius. 3. Substitute $r = 4.4$ into the formula: $$V = \frac{4}{3} \pi (4.4)^3$$ 4. Calculate the cube of the radius: $$4.4^3 = 4.4 \times 4.4 \times 4.4 = 85.184$$ 5. Substitute back: $$V = \frac{4}{3} \pi \times 85.184$$ 6. Multiply $\frac{4}{3}$ by $85.184$: $$\frac{4}{3} \times 85.184 = \frac{4 \times 85.184}{3} = \frac{340.736}{3}$$ 7. Show cancellation: $$\frac{\cancel{340.736}}{\cancel{3}} = 113.5787...$$ 8. So, $$V = 113.5787... \pi$$ 9. Multiply by $\pi \approx 3.1416$: $$V \approx 113.5787 \times 3.1416 = 356.87$$ 10. Round to the nearest hundredth: $$\boxed{356.87 \text{ mm}^3}$$ This is the volume of the sphere.