MathDB

A4

Part of Putnam 1938

Problems(1)

Putnam 1938 A4

Source:

8/20/2021
A notch is cut in a cylindrical vertical tree trunk. The notch penetrates to the axis of the cylinder and is bounded by two half-planes. Each half-plane is bounded by a horizontal line passing through the axis of the cylinder. The angle between the two half-planes is θ\theta. Prove that the volume of the notch is minimized (for given tree and θ\theta) by taking the bounding planes at equal angles to the horizontal plane.
Putnam