A watchdog is tied to the outside wall of a round building 20 feet in diameter. If the dog's chain is long enough to wind half way around the building, how large an area can the watchdog patrol?

According to http://mathworld.wolfram.com/GoatProblem.html the answer for a building of radius a and a chain of length L <= a*pi is

A=(pi*L^2)/2+(L^3)/(3*a)

and when L=a*pi this becomes (5/6)*(pi^3)*(a^2) which evaluates to 2583.85639 for a=10.

Posted by Richard on 2004-10-30 07:21:23