Math Paradox Breaking Calculus: Can You Fill the funnel's inside and coat its outside completely?

Imagine a funnel that stretches out forever into infinity. If you wanted to fill the inside completely to the brim with glowing molten iron, and then paint the entire outside of it red... which task requires more material? The Iron or The Paint? Most people guess they both take an infinite amount! But calculus proves a mind-bending paradox: Gabriel’s Horn has a FINITE volume (exactly pi) but an INFINITE surface area. This means you could perfectly fill
the entire infinite shape with pi cubic units of molten iron... but you don't have enough paint in the entire universe to coat the outside!

Resource:
Gabriel's horn. https://en.wikipedia.org/wiki/Gabriel%27s_horn

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Видео Math Paradox Breaking Calculus: Can You Fill the funnel's inside and coat its outside completely? канала Texas Little Apple