Gabriel’s horn — a shape with finite volume but infinite surface area

This leads to an apparent paradox called the painter’s paradox that was covered in <a href="https://graphicmaths.com/recreational/paradoxes/painters/" rel="noopener ugc nofollow" target="_blank">this article</a>. The paradox arises because the shape can be filled with a finite amount of paint (since it has a finite volume). But when it is full, the paint must be touching every part of its inner surface. Since the surface area is infinite, this implies that we have covered an infinite area with a finite amount of paint! See the linked article for a resolution to this paradox. In this article, we will prove that the shape has finite volume and infinite area. We will do this in two different ways, first using an infinite series of cylinders (similar to the way the problem was first solved by Evangelista Torricelli in the 17th century), and then using calculus. <a href="https://medium.com/recreational-maths/gabriels-horn-001077653cde">Visit Now</a>