Volume and Surface Area of Gabriel's Horn

Question

Could you fill Gabriel's Horn with paint? How much paint would it take? Could you paint the outside of Gabriel's Horn?

Answer 1

Paradoxically, Gabriel's Horn (or Torricelli's Trumpet) has finite volume (it can be filled) yet has infinite surface area (cannot be painted).

 

A detailed explanation is at

http://mathworld.wolfram.com/GabrielsHorn.html