SOLUTION: A square barn measures 14 meters on each side. A goat is tethered outside by a rope that is attached to one corner of the barn. The rope is 8 meters long. Suppose the rope is ma

Algebra ->  Circles -> SOLUTION: A square barn measures 14 meters on each side. A goat is tethered outside by a rope that is attached to one corner of the barn. The rope is 8 meters long. Suppose the rope is ma      Log On


   

Question 211733: A square barn measures 14 meters on each side. A goat is tethered outside by a rope that is attached to one corner of the barn. The rope is 8 meters long.
Suppose the rope is made twice as long. On how many sqaure meters of land is the goat now able to graze?
Lastly, an addition to the barn was built making it rectangular with dimensions 14 by 20 meters. On how many square meters of land is the goat now able to graze?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
In the first case, the barn cuts out one quarter of the circle of land that the goat can graze on, so the amount of land the goat can graze on would be three fourths the area of the circle.
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The area of the circle is pi%2A8%5E2 which equals 201.0619298 square meters.
One fourth the area of the circle is equal to 50.26548246 meters.
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The area the goat can graze on is:
201.0619298 square meters minus 50.26548246 square meters equals 150.7964474 square meters.
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In the second case, the barn still cuts off one fourth of the area that the goat can graze on but there are edges where the goat can graze that he was unable to do before.
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These edges are equal to one fourth the area of each of two smaller circles with a radius of 2 meters.
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The area of the larger circle is pi%2A16%5E2 which equals 804.2477193 square meters.
One fourth the area of the larger circle is equal to 201.0619298 square meters.
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The area of each smaller circle is pi%2A2%5E2 which equals 12.612.56637061 square meters.
One fourth the area of each smaller circle is equal to 3.141592654 square meters.
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The area the goat can graze on is three fourths the area of the large circle plus one fourth the area of each of the two small circles.
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That becomes:
804.2477193 square meters minus 201.0619298 square meters plus 2 * 3.141592654 square meters which equals 609.4689748 square meters.
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In the last case the barn is extended on one side to 20 feet.
That cuts out one of the corners, so the area the goat can graze on is now 606.3273821 square meters.
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A picture of each of these scenarios can be found at:
http://theo.x10hosting.com/
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click on problem number 211733
There may be more than one picture, so you'll probably see:
211733.1
211733.2
211733.3
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If it's not there when you look, wait one half hour and look again.
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