What is the formula for the volume of a cone?

The volume of a cone is calculated using the formula V = 1/3 π r² h, where r represents the radius of the base of the cone and h represents its height. In this formula, the fraction 1/3 accounts for the fact that a cone occupies one-third of the volume of a cylinder that has the same base area and height.

This means that for any cone, if you take the area of the circular base (which is found using a radius squared multiplied by π) and multiply it by the height, then divide that product by 3, you will get the volume of the cone. This relationship is essential in geometry as it helps to visualize and calculate the space that a cone occupies in three dimensions.

The other options do not accurately represent the correct volume for a cone. For instance, the first option represents the volume of a sphere, while the second option would suggest the volume of a cylinder (not accounting for the 1/3 reduction necessary for a cone). Similarly, the last option implies a different type of measurement again that does not conform to the volume formula of a cone. Thus, selecting the correct formula C ensures accurate calculations involving the volume of a cone.