Volume of a cone with radius r and height h is:

To find the volume of a cone, we compare it to a cylinder with the same radius $r$ and height $h$. 1. **Base Area**: The base of a cone is a circle. The area of this base is given by the formula: $$A = \pi r^2$$ 2. **Relationship to a Cylinder**: A cylinder with the same dimensions has a volume of $V_{cylinder} = \text{Base Area} \times \text{Height} = \pi r^2 h$. 3. **The Cone Factor**: In geometry, it is proven (through calculus or physical displacement experiments) that a cone occupies exactly one-third of the volume of a cylinder with the same base and height. 4. **Final Formula**: Multiplying the cylinder volume by $1/3$, we get: $$V = \frac{1}{3} \pi r^2 h$$ Therefore, the correct option is **(1/3) π r² h**.