How do you calculate the volume of a cone?

The volume of a cone is calculated using the formula for the volume of a three-dimensional shape. In this case, the correct formula is one third times pi times the radius squared times the height of the cone.

This formula comes from the general principle of finding volume for pyramidal shapes, where the volume is always one third the product of the area of the base and the height. The base of a cone is a circle, and the area of a circle is calculated as pi times the radius squared. Therefore, to find the volume of a cone, you take the area of the circular base (pi times radius squared), multiply it by the height of the cone, and then multiply that entire product by one third to account for the cone's tapered shape.

This relationship between the base area and height reflects how a cone is a tapering shape and differs from a cylinder, which would simply use the base area multiplied by the height without the one third factor.