How do you calculate the volume of a cone?

To calculate the volume of a cone, the correct formula is derived from the concept that a cone can be viewed as a three-dimensional figure that resembles a pyramid with a circular base. The general formula for the volume of a pyramid is one-third the base area times the height.

In the case of a cone, the base is a circle, and the area of a circle is expressed as (πr²), where (r) is the radius of the circular base. When finding the volume, you multiply the area of the base by the height (h) of the cone and then multiply that product by one-third, since a cone's volume is one-third of the volume of a cylinder with the same base and height. Thus, the volume formula for a cone becomes:

[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \pi r^2 h. ]

This clearly indicates that the correct way to find the volume will yield a result that involves multiplying by one-third, making the correct answer aligned with the formula provided in the correct choice. Understanding this foundational geometry principle is essential when calculating volumes