min path on surface of cylindrical glass
Source: Spanish Mathematical Olympiad 1981 P2
December 23, 2022
geometry3D geometrycylindergeometric inequality
Problem Statement
A cylindrical glass beaker is cm high and its circumference rim is cm wide . Inside, cm from the edge, there is a tiny drop of honey. In a point on its outer surface, belonging to the plane passing through the axis of the cylinder and for the drop of honey, and located cm from the base (or bottom) of the glass, there is a fly.
What is the shortest path that the fly must travel, walking on the surface from the glass, to the drop of honey, and how long is said path?[hide=original wording]Un vaso de vidrio cil´ındrico tiene 8 cm de altura y su borde 12 cm de circunferencia. En su interior, a 3 cm del borde, hay una diminuta gota de miel. En un punto de su superficie exterior, perteneciente al plano que pasa por el eje del cilindro y por la gota de miel, y situado a 1 cm de la base (o fondo) del vaso, hay una mosca.
¿Cu´al es el camino m´as corto que la mosca debe recorrer, andando sobre la superficie del vaso, hasta la gota de miel, y qu´e longitud tiene dicho camino?