What is the volume formula for a right circular cone?

The formula for the volume of a right circular cone is indeed represented by ( V = \frac{1}{3} \pi r^2 h ). This formula is derived from the concept that the volume of a cone is one-third the product of the area of its base and its height.

To understand why this is the case, consider that the base of a cone is a circle. The area ( A ) of a circle is calculated using the formula ( A = \pi r^2 ), where ( r ) is the radius of the circle. When calculating the volume of any three-dimensional object, the general approach involves multiplying the area of the base by the height of the shape.

For a cone, because it tapers to a point, the volume is scaled down by a factor of one-third, which signifies that it occupies a smaller space compared to a cylinder of the same base and height. Therefore, the correct volume formula incorporates this scaling factor, leading to the final expression ( V = \frac{1}{3} \pi r^2 h ).

In summary, this formula accurately accounts for the shape and geometric properties of a right circular cone, correlating the volume to the circular area of its base