So, I am sure y'all familiar with Gabriel's horn, and when I looked up for the surface of it, the integral is based of a section of a cone but not a cylinder, even though a cylinder was used for the volume.
Moreover, by using a cylinder, the fact that the surface is infinite does not change.
Then why is a section of cone used for the surface and not the volume, and why a cylinder is used for the volume and not for the surface in order to calculate the surface and volume of Gabriel's horn ?
So, this question was already asked in a way, by this post, thus I mark my question as solved
link to the already asked and answered question : link to the post
thanks to Andrew D. Hwang for the link to this question