What is the volume formula for a cone?

The formula for the volume of a cone is given by V = (1/3)πr²h. This formula captures the relationship between the radius of the base (r), the height of the cone (h), and the volume (V) of the cone itself.

The factor of 1/3 indicates that the volume of a cone is a third of the volume of a cylinder with the same base radius and height. In a cylinder, the volume is calculated by multiplying the area of the base (which is πr²) by the height (h), resulting in V = πr²h. Since a cone occupies exactly one-third of the space of such a cylinder, it makes sense that the volume formula incorporates that fraction.

Understanding this concept is foundational in geometry, as it allows for the calculation of volumes for various shapes, particularly in applications such as engineering and physical sciences, where precise measurements are critical.