Lampshade
Source:
September 5, 2010
geometry3D geometrygeometry unsolved
Problem Statement
A lampshade is part of the surface of a right circular cone whose axis is vertical. Its upper and lower edges are two horizontal circles. Two points are selected on the upper smaller circle and four points on the lower larger circle. Each of these six points has three of the others that are its nearest neighbors at a distance from it. By distance is meant the shortest distance measured over the curved survace of the lampshade. Prove that the area of the lampshade is where