Two cylinders of equal radius have their axes meeting at right angles. Find the radius of the cylinders if the volume of the common portion is 144 cu.cm.

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.

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....