jmc

The radius of the cone is half the side length of the triangle, which is 6 cm. The height of the cone is an altitude of the triangle, which is $6\sqrt{3}$. Therefore, the volume of the cone is $$\frac{1}{3}\cdot (6^2\pi )(6\sqrt{3})=\boxed{72\pi \sqrt{3}}\text{ cubic centimeters}.$$