SOLUTION: A cow is tethered to one corner of a square barn, 10 feet by 10 feet, with a rope 100ft long. What is the maximum grazing area for the cow. I know that the answer is 31,145.15 ft s

Question 131013: A cow is tethered to one corner of a square barn, 10 feet by 10 feet, with a rope 100ft long. What is the maximum grazing area for the cow. I know that the answer is 31,145.15 ft squared. I figured out that the left side of the circle has an area of 49348feet. the other semicircular shape - it is not a true semicircle- is split up into three four areas. a quarter circle on the bottom right, sector on the upper right a sector on the right side and a triangle between those two sectors.
please show all your work.
thank you!
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
Question???? Is the cow inside or outside of the barn?
We'll assume it is outside the barn because the inside is too easy.
---------------------------------
First we have an area that is 3/4 of a circle with a radius of 100 ft.
area=(3.14*100^2)*3/4=(3.14*10,000)*3/4=31,400*3/4=23,550 ft^2.
now we have a quarter circle with a raduis of 90 ft.
area=(3.14*90^2)/4=(3.14*8,100)/4=25,434/4=6,358.5 ft^2.
as an esimate of the remaining 2 slivers of 5*80+5*90=400+450=950 ft^2 (minus a tad)
adding up these pieces I get 23,550+6,358.5+950=30,858.5 ft^2 (minus the tad)

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