What is the formula for the volume of a cone?

The volume of a cone is calculated using the formula ((1/3)πr²h), where (r) represents the radius of the circular base, and (h) is the height of the cone. This formula derives from the principle that the volume of a cone is one-third the volume of a cylinder with the same base area and height.

To break it down: the base area of the cone is given by the area of the circle, which is (πr²). When you multiply this area by the height (h), you have the total volume of the cylinder. However, since a cone occupies only one-third of that volume, the factor of ((1/3)) is included in the formula.

This understanding of the relationship between cones and cylinders underscores why ((1/3)πr²h) is the correct formula for finding the volume of a cone, making it essential in various applications in geometry and engineering.