Analysis: ants are required to crawl the shortest distance, and the side of the cone needs to be unfolded, and then the result is obtained according to the "shortest line segment between two points".

Answer: solution: from the meaning of the question, the diameter of the bottom circle AB=4,

So the circumference of the bottom is equal to 4 π.

Let the fan-shaped central angle of the expanded cone side be n,

According to the fact that the perimeter of the bottom is equal to the arc length of the unfolding fan, it is 4π= 2nπ×6/360.

The solution is n = 120,

So ∠ APD = 120 ÷ 2 = 60,

According to Pythagorean theorem, the root 3 of AD=3 is obtained.

So the shortest distance for ants to crawl is 3.