Tethered Bull Problem

Let a bull be tethered to a silo whose horizontal Cross-Section is a Circle of Radius $R$ by a leash of length $L$. Then the Area which the bull can graze if $L\leq R\pi$ is

$$A={\pi L^2\over 2}+{L^3\over 3R}.$$

References

Hoffman, M. E. ``The Bull and the Silo: An Application of Curvature.'' Amer. Math. Monthly 105, 55-58, 1998.