3.6. Znayka cut out a semicircle from paper. Neznaika marked a point $M$ on the diameter $A B$ of this semicircle and cut off two semicircles from Znayka's semicircle with diameters $A M$ and $M B$. The area of the remaining figure turned out to be $16 \pi^{3}$. Find the length of the part of the chord lying inside it, passing through point $M$ perpendicular to $A B$. If necessary, round the answer to two decimal places.
Answer: 25.13 (exact value: $8 \pi$).