Cut and spread the cylinder along the high line, which is equivalent to a rectangle.

Height 12cm, bottom radius 3cm.

The length of a rectangle is the circumference of the bottom of the cylinder =2πr=2*3*3= 18 cm (π is 3 in the title).

The width of a rectangle is the height of a cylinder = 12 cm.

So the AB distance is the diagonal length drawn in the figure = under the root sign (9? + 12? ) =15cm

So the shortest crawling distance is 15 cm.

PS: I saw the picture drawn by LZ and found that it was wrong before. Point B should really be at the long midpoint, and the triangle is a right triangle composed of 9 12 and 15.