Answer
If your concern is the apparent paradox about a infinite length of paint and a finite area, then you might want to consider what Wikipedia says on about Gabriel's horn with an infinite area of paint and a finite volume, and then take it down a dimension:
Since the Horn has finite volume but infinite surface area, it seems
that it could be filled with a finite quantity of paint, and yet that
paint would not be sufficient to coat its inner surface – an apparent
paradox. In fact, in a theoretical mathematical sense, a finite amount
of paint can coat an infinite area, provided the thickness of the coat
becomes vanishingly small "quickly enough" to compensate for the
ever-expanding area, which in this case is forced to happen to an
inner-surface coat as the horn narrows. However, to coat the outer
surface of the horn with a constant thickness of paint, no matter how
thin, would require an infinite amount of paint. Of course, in
reality, paint is not infinitely divisible, and at some point the horn
would become too narrow for even one molecule to pass.
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