Putnam 1938 A4
Source:
August 20, 2021
Putnam
Problem Statement
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 . Prove that the volume of the notch is minimized (for given tree and ) by taking the bounding planes at equal angles to the horizontal plane.