This paradox is not original
Consider a horn with an open side, which becomes thinner and thinner as the horn's length approaches infinity
Is the amount of paint is needed to cover the inside of the horn finite or infinite?
Since the inside of the horn has infinite surface area, and the paint must cover the infinite surface area, the amount of paint is infinite
However, the horn has finite volume as it closes at infinity. Thus, if we took a can of paint of the same volume as the horn, and poured it into the horn, the paint would cover the entire inner surface area. Thus, the amount of paint is finite
Thus, arises the paradox!