The top of flagpole, the broken part and the bottom of flagpole form a right triangle.

The length from the top of the flagpole to the fracture = the length of the hypotenuse,

The length of the hypotenuse? =8? + 14? =260

Length of hypotenuse =√260=2√(65) (m),

Then before the flagpole broke, it was 8+2√(65) meters high.

2)

There is no diagram, assuming that the point A of the lower bottom surface is just opposite to the point B of the upper bottom surface, and the cylindrical side surface is unfolded into a rectangle,

Connecting AB is the shortest path for ants to crawl,

AB, height, half the length of a rectangle constitutes a right triangle, and the length of the rectangle = half the perimeter of the base:

AB？ =(2*3*π/2)? + 12? =9(π+ 16)

AB=3√(π+ 16) (cm)