Napkin Ring Problem
In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere. It is a counterintuitive fact that this volume does not depend on the original sphere's radius but only on the resulting band's height. The problem is so called because after removing a cylinder from the sphere, the remaining band resembles the shape of a napkin ring. Statement Suppose that the axis of a right circular cylinder passes through the center of a sphere of radius R and that h represents the height (defined as the distance in a direction parallel to the axis) of the part of the cylinder that is inside the sphere. The "band" is the part of the sphere that is outside the cylinder. The volume of the band depends on h but not on R: V=\frac. As the radius R of the sphere shrinks, the diameter of the cylinder must also shrink in orde ...
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Sphere Bands
A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a