How is the volume of a cone calculated?

The volume of a cone is calculated using the formula that includes one-third of the base area multiplied by the height. The formula is given as one-third times π times the radius squared times the height. This reflects the geometric relationship between the cone and a cylinder; a cone occupies one-third of the volume of a cylinder with the same base and height.

In the context of the other options, the first option represents the formula for the volume of a cylinder, where the volume is simply the area of the base (π times radius squared) multiplied by the height. The third option suggests a formula that incorrectly factors in the height squared rather than height, which is not applicable for calculating volume in three-dimensional space. Lastly, the fourth option presents the volume of a sphere rather than a cone, which signifies a complete misunderstanding of the geometric shapes and their respective volume calculations.

Thus, option B accurately captures the essential components required to derive the volume of a cone, encapsulating the importance of both the base area and the height in the calculation.