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?

First, the curve is not a cardioid, it is an involute of the circle.

Second, I did an approximation of the area by enclosing one "horn" in a matching rectangle and computing the area of the two corners which, value doubled, were subtracted, along with the building area, from the area of a rectangle enclosing both horns. This value was added to the area of the semicircle, giving an approximate total "patrol area" of 2329.771442 square feet.

Now, I feel ever so better. Hugs. - CeeAnne -

Posted by CeeAnne on 2004-10-30 05:45:30