Consider a right circular cone that has a radius of 5 cm and a height of 12 cm. You are tasked with finding the volume of this cone. The formula for the volume $V$ of a cone is given by:
$$ V = \f\frac{1}{3} \pi r^2 h $$
where $r$ is the radius and $h$ is the height of the cone. Calculate the volume of the cone, rounding to the nearest cubic centimeter.