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A cow is tethered by a 120-ft rope to the inside corner of an L-shaped building, as shown in the figure. Find the area that the cow can graze. (Let 

a = 30 ft, b = 60 ft, c = 120 ft, d = 70 ft, and e = 60 ft.

 Round your answer to the nearest whole number.)

 Oct 28, 2020
 #1
avatar+28021 
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First the cow gets to meander about 1/4 of a full circle    radius 120 ft     1/4  pi (1202)

  when it gets up just right of 'a'  the rope is now shorter by length 'b'  so   60 ft

       mooster gets 1/4 of a circle   radius 60 ft         1/4 pi (602)

             gets to the left of 'a' rope is shorter again by 'a'       so  30 ft

                   area is 1/4 of a circle radius 30    1/4 pi 302

 

When it gets to intersection of d and e the rope gets 70 ft shorter    so   50 ft long

   1/4 of circle radius 50 ft       1/4 pi 502  

 

TOTAL area is the sum of the REDS above......

 Oct 28, 2020

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