Truncated Cylinder

To get the radius of the circle found on this crossing cylinders, recall that:

where $r$ is the radius of the circle found on the base of the cylinders and $V$ is the volume of the common portion of crossing cylinders shown above.

With that in mind, we have:

$$V = \frac{16}{3}r^3$$ $$144 \space cm^3 = \frac{16}{3}r^3$$ $$r = 3 \space cm$$

Therefore, the radius of the circle found on the bases of crossing cylinders is $\color{green}{3 \space cm}$.

Alternate solutions are encouraged....