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# i have 200m of fencing and i am trying to get the largest area with that amount of fencing

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I have 200m of fencing and I am trying to get the largest area with that amount of fencing

Aug 16, 2017

#1
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The max area is always a square:

P = 200, s = 200/4 = 50, A = 50*50 = 2500 square meters.

Aug 16, 2017
#2
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No,the max area is always a circle.(And the  the max volume enclosed by min surface area is always a sphere.)

Fence length  = 200 metres      which can enclose a circular area of

pi (r^2).                 So find r,the radius.

Circumference  = 200   =  2 pi(r)

pi (r)                 =100

radius  is  100/(pi)         Area is  pi   X { (100)^2} /(pi^2) }

Area = (100^2)  /pi      = 3183.098   which is greater than the area of the square.

The most area efficient shape is a circle.  The most volume efficient shape is a sphere.That's why planets are not cube shaped.

Aug 16, 2017
#3
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The guest is correct......a circle will give us the greatest area

Aug 16, 2017
edited by CPhill  Aug 16, 2017