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Napkin ring problem - mklabgr - 06-27-2026 Napkin ring problem Summary The Napkin Ring Problem is one of the most surprising puzzles in geometry. Imagine drilling a cylindrical hole straight through the center of a sphere, leaving behind a ring-shaped solid that looks like a napkin ring. Intuition suggests that a larger original sphere would leave behind more material, but the opposite is true: if the remaining ring has the same height, its volume is always exactly the same, regardless of the sphere's original size.  In other words, the volume depends only on the height of the remaining band, making it a beautiful example of how mathematics can produce results that seem impossible at first glance but follow perfectly from geometric principles.  ARTICLE