Integrating under the curve shows that the volume approaches pi, while the surface area is greater than two pi times the natural log of the upper bound of integration.
This figure is formed by graphing y=(1/x) with a domain restriction to avoid the asymptote, then rotating it in 3 dimensions around the x axis. Integrating under the curve shows that the volume approaches pi, while the surface area is greater than two pi times the natural log of the upper bound of integration. This is sometimes called the painter's paradox (*) as painting an infinite area requires an infinite amount of paint, but filling the figure requires a finite volume of paint. FTP, name this figure with infinite surface area, but finite volume.
This figure is formed by graphing y=(1/x) with a domain restriction to avoid the asymptote, then rotating it in 3 dimensions around the x axis.
{Gabriel's horn} or {Torricelli's trumpet} (accept “{painter's paradox}” early)