1960 IMO Problems/Problem 6

Revision as of 13:59, 28 October 2007 by Inscrutableroot (talk | contribs) (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 $V_1$ 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

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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
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