What is the formula for the volume of a cone?

The volume of a cone is calculated using the formula V = 1/3 B•h, where B represents the area of the base and h is the height of the cone. This formula is derived from the fact that a cone can be thought of as a pyramid with a circular base. The volume of a pyramid is given by the formula V = 1/3 B•h, which is applicable to any pyramid shape, including those with a circular base like a cone.

In this context, B specifically refers to the area of the base of the cone, which would be calculated as πr² for a cone with a circular base where r is the radius. Consequently, incorporating this base area into the volume formula confirms that the cone occupies one-third of the space compared to a cylinder with the same base area and height, making the formula not only essential but also reflective of geometric principles.

Other options related to the volume of a cone either misrepresent the relationship between the dimensions of the cone or describe the volume for different shapes, leading to incorrect calculations. Hence, the given formula effectively captures the volume of a cone accurately, supporting the understanding of its geometric properties.