Difference between revisions of "1960 IMO Problems/Problem 6"

(Problem)
m (Problem)
Line 1: Line 1:
 
==Problem==
 
==Problem==
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 <math>V_1</math> be the volume of the cone and <math>V_2</math> be the volume of the cylinder.
+
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 <math>V_1</math> be the volume of the cone and <math>V_2</math> be the volume of the cylinder.
  
 
a) Prove that <math>V_1 \neq V_2</math>;
 
a) Prove that <math>V_1 \neq V_2</math>;

Revision as of 13:59, 28 October 2007

Problem

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 $V_1$ be the volume of the cone and $V_2$ be the volume of the cylinder.

a) Prove that $V_1 \neq V_2$;

b) Find the smallest number $k$ for which $V_1 = kV_2$; for this case, construct the angle subtended by a diamter of the base of the cone at the vertex of the cone.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

1960 IMO (Problems) • Resources
Preceded by
Problem 5
1 2 3 4 5 6 Followed by
Final Question
All IMO Problems and Solutions
Invalid username
Login to AoPS