Napkin Ring Problem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, it is somewhat surprising that the volume of a band of specified height around a sphere does not depend on the sphere''s radius. Specifically, suppose the axis of a right circular cylinder passes through the center of the sphere and the height (defined as distance in a direction parallel to the axis) of the part of the boundary of the cylinder that is inside the sphere is h, and the radius of the sphere is R. The "band" is the part of the sphere that is outside the cylinder.…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, it is somewhat surprising that the volume of a band of specified height around a sphere does not depend on the sphere''s radius. Specifically, suppose the axis of a right circular cylinder passes through the center of the sphere and the height (defined as distance in a direction parallel to the axis) of the part of the boundary of the cylinder that is inside the sphere is h, and the radius of the sphere is R. The "band" is the part of the sphere that is outside the cylinder.