Of course, in both cases it is interior - volume respectively area - and boundary - surface area respectively boundary length - but that is not the same thing a

Of course, in both cases it is interior - volume respectively area - and boundary - surface area respectively boundary length - but that is not the same thing as area and volume of a two dimensional object. The analog for Gabriel's horn would be volume and four dimensional hypervolume which is of course also zero because it is a three dimensional object. The paradox goes from interior to boundary, what mkagenius suggested is taking the interior one dimension up.