A farmer wishes to enclose the maximum possible area with 100 meters of fence. The pasture is bordered by a straight cliff, which may be used as part of the fence. What is the maximum area that can be enclosed?

A circle is the figure with the highest amount of area. Since the cliff can be used as part of the fence, we only need to construct a semicircle with circumference 100 meters.

Calculating backwards using a circumference of 200 meters (for an entire circle) the radius of the circle is 100/pi meters. This gives a total area of (100/pi)*(100/pi)*pi*(1/2) square meters, or more concisely 5000/pi square meters.

Posted by Eric on 2004-06-18 09:56:57