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maximize cylinder volume

Source: France 1994 P2

May 7, 2021

inequalitiesgeometryGeometric Inequalities3D geometry

Problem Statement

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

, cuts

\Sigma

at a circle

C

. We denote by

C'

the orthogonal projection of

C

onto

P

. Find the position of

Q

for which the cylinder with bases

C

and

C'

has the maximum volume.

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