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?

(In reply to WD-40 please! - spoilers by nikki)

I think you logic is right, but your simplification of S is errored.

S = L-W = pi*D/2 - pi*D*theta/360
             = pi*D/2 - pi*D/2*theta/180
             = pi*D/2(1-theta/180)

Area B = Integral S along theta from theta = 0 to 180
             = pi*D/2*(integral 1-theta/180 from 0 to 180)
             = pi*D/2*(theta-theta^2/360 from 0 to 180)
             = pi*D/2*[(180-180^2/360)-(0-0)]
             = 2827.4333

Area A = 1/2*pi*D^2 = 50*pi^3 = 1550.314

Patrol Area = A + 2B = 7205.181

Posted by Christian on 2004-10-28 16:34:21