Circular Field, Cow, and Length of Rope
Date: 9/11/96 at 13:57:25 From: Anonymous Subject: Circular Field, Cow, and Length of Rope If a cow is anchored by a chain to the perimeter of a circular field of grass with the other end of the chain tied around its neck; given that the field has a diameter of 10 feet, how long does the chain have to be for the cow to eat half the grass? Is there a ratio between the radius and the length of chain? Please detail the explanation as much as possible. Thank you.
Date: 9/11/96 at 16:36:42 From: Doctor Ken Subject: Re: Circular Field, Cow, and Length of Cow's Rope Hello - It just so happens that we've answered cow questions like this before (complete with pictures!), so you can browse our archives to see the answers. Point your web browser at the address at the bottom of this message, and go to the High School Geometry section. However, these problems are a little different from the one you propose. Let L be the length of the chain. Then the area that the cow can graze is given by 100 Pi - (10-L)^2 Pi. (the whole area minus the inner circle) If this is half of the area of the entire field, then it is equal to 50 Pi, so we get 100 Pi - (10-L)^2 Pi = 50 Pi. Solve that, and you'll have your answer. -Doctor Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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