Napkin Ring puzzle (hole through a sphere)
A classic puzzle:
If you’s one of them fancy types, you might use napkin rings at your supper table. Consider a very simple napkin ring that is produced by drilling a cylindrical hole through a sphere. The centerline of the hole intersects the centerpoint of the sphere. The height h of the cylindrical surface is 6 cm. Find the volume of this simple napkin ring.
By tinkering with the GeoGebra construction, can you develop an intuitive sense of why neither the radius of the sphere nor the radius of the hole needed to be specified in the problem statement?
Using calculus, can you prove that the volume depends on neither the radius of the sphere nor the radius of the hole?
~ ~ ~ ~ ~ ~ ~
The various sliders and checkboxes in the construction below should be self-evident.
The "volume" checkbox will display a decimal approximation. For a derivation of how it is calculated, do a web search of "napkin ring puzzle."