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?

Forget parametric. The algebraic expression (gotten from the parametric) for the cardioid is (x^2+y^2-R^2)^2 which equals 4R^2{(x-R)^2+y^2}, so the length of the curve shouls be 8R and the area should be 6piR^2. The dog's chain behaves just like a circle rolled around another circle. Do you remember how a coin rolled around another coin the same size makes two revolutions? The dog's chain is like one revolution. His chain should be piR in length, that is 31.41592654 feet ... see how it all fits?

Posted by CeeAnne on 2004-10-28 15:55:26