What is the formula for the volume of a cone?

The formula for the volume of a cone is indeed V = 1/3πr²h. This formula is derived from the general principle of finding the volume of a three-dimensional shape. In the case of a cone, the volume is calculated by taking the area of the base of the cone, which is a circle (given by πr², where r is the radius), and multiplying it by the height of the cone (h). Since a cone is essentially a pyramid with a circular base, its volume is one-third of that of a cylinder with the same base and height. This is why the formula includes the factor of 1/3.

The other options represent formulas for different shapes or calculations:

• The formula for lwh represents the volume of a rectangular prism, not a cone.
• The formula 1/2 bh corresponds to the area of a triangle, which does not apply to the volume of a cone.
• The formula πr²h refers to the volume of a cylinder, not accounting for the one-third factor necessary for a cone's volume.

Thus, the correct option accurately captures the specific relationship between a cone's base area and height in the context of its volume calculation.