What is the length described in surface tension?

[goggles31]

https://web.mst.edu/~numbere/CP/CHAPTER 3.htm

I have trouble understanding why the length used in 3.1.1 is pir^2. My notes don't explain what length we use either.

 

[Vanadium 50]

πr² is not a length. That may be the source of the confusion.

 

[goggles31]

πr² is not a length. That may be the source of the confusion.

Sorry I meant 2pir. Specifically the term σcosθ(2pir).