Problem 2

Part of 1994 French Mathematical Olympiad

Problems(1)

maximize cylinder volume

Source: France 1994 P2

Let be given a semi-sphere

\Sigma

whose base-circle lies on plane

p

. A variable plane

Q

, parallel to a fixed plane non-perpendicular to

P

\Sigma

C

C'

the orthogonal projection of

C

P

. Find the position of

Q

for which the cylinder with bases

C

C'

has the maximum volume.

inequalitiesgeometryGeometric Inequalities3D geometry