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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....