1. The problem is to understand and use the formula for the volume of a sphere, which is given by $$V = \frac{4}{3} \pi r^3$$ where $V$ is the volume and $r$ is the radius of the sphere. 2. This formula calculates the volume inside a sphere based on its radius. The constant $\pi$ (pi) is approximately 3.14159. 3. To use this formula, you need to know the radius $r$ of the sphere. 4. For example, if the radius is 3 units, substitute $r=3$ into the formula: $$V = \frac{4}{3} \pi (3)^3$$ 5. Calculate the cube of the radius: $$3^3 = 27$$ 6. Substitute back: $$V = \frac{4}{3} \pi \times 27$$ 7. Multiply $\frac{4}{3}$ by 27: $$\frac{4}{3} \times 27 = \cancel{\frac{4}{3}} \times \cancel{27} = 4 \times 9 = 36$$ 8. So the volume is: $$V = 36 \pi$$ 9. If you want a decimal approximation, multiply 36 by $\pi \approx 3.14159$: $$V \approx 36 \times 3.14159 = 113.097$$ 10. Therefore, the volume of a sphere with radius 3 units is approximately 113.097 cubic units. This formula is fundamental in geometry and physics when dealing with spherical objects.