1. **Problem:** If the volume and surface area of a sphere are numerically equal, find its radius. 2. **Formulas:** - Volume of a sphere: $$V = \frac{4}{3} \pi r^3$$ - Surface area of a sphere: $$A = 4 \pi r^2$$ 3. **Given:** $$V = A$$ 4. **Set up the equation:** $$\frac{4}{3} \pi r^3 = 4 \pi r^2$$ 5. **Simplify by dividing both sides by $$4 \pi r^2$$ (assuming $$r \neq 0$$):** $$\cancel{\frac{4}{3}} \cancel{\pi} \frac{r^3}{\cancel{r^2}} = \cancel{4} \cancel{\pi} \cancel{r^2}$$ $$\frac{4}{3} r = 4$$ 6. **Solve for $$r$$:** $$r = \frac{4 \times 3}{4} = 3$$ 7. **Answer:** The radius of the sphere is **3 units**. This means when the volume and surface area of a sphere are equal in numerical value, the radius must be 3 units.