2006 China Second Round Olympiad Test 1 #10
Source:
September 28, 2014
geometry3D geometrysphere
Problem Statement
Suppose four solid iron balls are placed in a cylinder with the radius of 1 cm, such that every two of the four balls are tangent to each other, and the two balls in the lower layer are tangent to the cylinder base. Now put water into the cylinder. Find, in , the volume of water needed to submerge all the balls.