Question

Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height h. Which ring has more wood in it?

Answer 1

The volume of wood in both napkin rings is the same if the height of the napkin rings is equal, regardless of the original size of the wooden balls or the diameter of the holes drilled through them.

Step-by-step explanation:

The question asks which napkin ring has more wood in it, given that both rings have the same height h and are made from wooden balls of different diameters with holes also of different diameters drilled through them. This is a geometry problem that involves understanding the volume of the remaining wood after drilling holes through spherical objects.

In this case, despite the initial size of the wooden balls and the size of the holes drilled, if the height h of the napkin rings is the same, the volume of wood in both napkin rings will also be the same. This is a surprising result that comes from the formula for the volume of a spherical shell, which depends only on the height of the shell and not on the original size of the sphere or the size of the hole.