Why Is Projected Area More Relevant Than Surface Area in Physics?

[Rahul Manavalan]

I wonder why projected area has been of much interest among physics communities, while the surface area could well be the solution unless any complex geometries are involved.
The question popped up in my head when the surface tension in a water jet was derived. Clearly the jet has a circular cross section.
Why not the curved surface area 4*(pi*r^2).
Other instance was when dealing with a bearing area calculation.
This puzzles me a great deal.
Hope someone could show me a way.

 

[Nidum]

In practical applications it usually comes down to components of forces acting on curved surfaces summing in one direction and cancelling in another direction .