1960 IMO Problems/Problem 6
Consider a cone of revolution with an inscribed sphere tangent to the base of the cone. A cylinder is circumscribed about this sphere so that one of its bases lies in the base of the cone. Let be the volume of the cone and be the volume of the cylinder.
a) Prove that ;
b) Find the smallest number for which ; for this case, construct the angle subtended by a diamter of the base of the cone at the vertex of the cone.
This problem needs a solution. If you have a solution for it, please help us out by.
|1960 IMO (Problems) • Resources|
|1 • 2 • 3 • 4 • 5 • 6||Followed by|
|All IMO Problems and Solutions|