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France Contests
French Mathematical Olympiad
1997 French Mathematical Olympiad
Problem 2
Problem 2
Part of
1997 French Mathematical Olympiad
Problems
(1)
maximal volume of a cylinder in region
Source: French MO 1997 P2
4/10/2021
A region in space is determined by a sphere with center
O
O
O
and radius
R
R
R
, and a cone with vertex
O
O
O
which intersects the sphere in a circle of radius
r
r
r
. Find the maximum volume of a cylinder contained in this region, having the same axis as the cone.
3D geometry
geometry