There is a big field full of green grass. At its centre is a circular fence, of radius R. a cow is tied to the circumference of the fence using a rope whose length is exactly 2[tex]\Pi[/tex]R. Now, the cow starts eating the grass. we have to find the maximum area of the grass it can eat. the cow can not enter into the circular region bounded by the fence, which is solid.(adsbygoogle = window.adsbygoogle || []).push({});

MY ATTEMPT AT THE SOLUTION:

the cow can eat all the grass located in a semicircular region of radius equal to the rope length, lying on the opposite side of the tangent drawn at the point of tying...

so that adds [tex]\Pi[/tex]^3 x R^2 sq units of grass to the cow's account.

once the cow finishes this it crosses the tangent and the moment it does so the rope starts winding at the fence. let us assume that a length of rope subtending an angle [tex]\theta[/tex] is now wound. then L-R[tex]\theta[/tex] is the temporary radius of the semicircle where the cow can graze. but it is not possible to find out the area beacuse we will inevitably count a patch of area several times..... i have tried hard and am unable to find my way... help will be thankfully received....

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# Homework Help: Cow Eats Grass!

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