Difference between revisions of "1960 IMO Problems/Problem 6"
m (→See Also) |
m (→See Also) |
||
Line 11: | Line 11: | ||
==See Also== | ==See Also== | ||
− | {{ | + | {{IMO7 box|year=1960|num-b=5|num-a=7}} |
Revision as of 19:04, 15 September 2012
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 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.
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) | ||
Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 • 7 | Followed by Problem 7 |