The slant height of a cone is 13 cm, and the height from the vertex to the center of the base is 12 cm. What is the number of cubic centimeters in the volume of the cone? Express your answer in terms of $\pi$.
We create a right triangle with the slant height as the hypotenuse, the height from the vertex to the center of the base as one of the legs, and a radius as the other leg.  By Pythagorean theorem, the radius measures $\sqrt{13^2-12^2}=5$ cm.  It follows that the volume of the cone is $(1/3)\pi(5^2)(12)=\boxed{100\pi}$.