A round pizza is $\frac13$ of an inch thick and has a diameter of 12 inches. It is cut into 12 congruent pieces. What is the number of cubic inches in the volume of one piece? Express your answer in terms of $\pi$.
The entire pizza has radius 6 inches and volume $\pi (6^2)(1/3) = 12\pi$ cubic inches.  One slice has 1/12th this volume, or $\boxed{\pi}$ cubic inches.