A wooden cube, whose edges are one centimeter long, rests on a horizontal surface. Illuminated by a point source of light that is \(x\) centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface. The area of a shadow, which does not include the area beneath the cube is 48 square centimeters. Find the greatest integer that does not exceed \(1000x\).

(第十四届AIME1996 第4题)