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?

The maximum area that could be enclosed is where the fence was that of a semi-circle.

As the circumference of a circle is 2*pi*R, such that R is the circle's radius, the fence-line's semi-circular arc length would be pi*R. By setting pi*R = 100 meters, the radius (R) is equal to 100/pi meters.

The area of the semi-circle of radius R is (1/2)*pi*R².
With the given radius, 100/pi meters, the area of the pasture would then be:  pi*(100/pi)²/2 = 5000/pi meters²
(approximately 1591.5494309189534 meters²).

Edited on November 7, 2008, 7:44 am

Posted by Dej Mar on 2008-11-07 07:42:09