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.

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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....