Question

A cow is tethered to one corner of a barn, 10 feet by 10 feet, with a rope 100 feet long. What is the cows maximum grazing area?

Answer 1

Question???? Is the cow inside or outside of the barn?

We'll assume it is outside the barn because the inside is too easy.

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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)