SOLUTION: Could you please help me with this problem? Would greatly appreciate it! A cow is tied by a 25 meter rope to a rectangular barn. The dimensions of the barn are 20 m x 15 m. The

Algebra ->  Circles -> SOLUTION: Could you please help me with this problem? Would greatly appreciate it! A cow is tied by a 25 meter rope to a rectangular barn. The dimensions of the barn are 20 m x 15 m. The       Log On


   

Question 1190844: Could you please help me with this problem? Would greatly appreciate it!
A cow is tied by a 25 meter rope to a rectangular barn. The dimensions of the barn are 20 m x 15 m. The rope is fastened to a hook that is in the center of the shorter side of the barn. What is the total area she can graze if she cannot travel into the barn?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A cow is tied by a 25 meter rope to a rectangular barn.
The dimensions of the barn are 20 m x 15 m.
The rope is fastened to a hook that is in the center of the shorter side of the barn.
What is the total area she can graze if she cannot travel into the barn?
:
Draw this out, roughly to scale, it will make sense to you then.
You can see that the area at the end of the barn is a semi circle with a radius of 25 meters. Find this area
A = 1%2F2pi%2A25%5E2
A = 981.75 sq/m, area of the semi circle portion
:
Two quarter circle areas, that the radius is limited by the barn, is the rest of the grazing area
It is tied to the middle of the end of the barn, therefore
radius = 25 - 15/2 = 17.5m
find the area of the quarter cicle with this radius
A = 1%2F4pi%2A17.5%5E2
A = 240.5 sq/m
The other side of the barn is the same therefore we have a total
981.75
240.50
240.50
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1,462.75 sq/m is the total grazing area