SOLUTION: A goat is tied to one of the corners of a rectangular barn on a rope that is 50 feet long. The dimensions of the barn are 40 feet by 30 feet. Assuming that the goat can graze whe

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Question 551049: A goat is tied to one of the corners of a rectangular barn on a rope that is 50 feet long. The dimensions of the barn are 40 feet by 30 feet. Assuming that the goat can graze wherever its rope allows it to reach, what is the square footage of the grazing area for the goat?
Found 3 solutions by mathstutor494, Edwin McCravy, AnlytcPhil:
Answer by mathstutor494(120) About Me  (Show Source):
You can put this solution on YOUR website!
As the rope covers entire area of the barn, goat will 40*30= 1200 Sq Ft

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
That's wrong. Check this site later.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
A goat is tied to one of the corners of a rectangular barn on a rope that is 50
feet long.  The dimensions of the barn are 40 feet by 30 feet.  Assuming that
the goat can graze wherever its rope allows it to reach, what is the square
footage of the grazing area for the goat?



The area of a circle is pr²

The grazing area consists of 

1. three quarters of a big 50ft-radius circle, which has area

    3%2F4·p(50)² = 3%2F4·2500p square feet = 1875p square feet. 

2. one quarter of a 20ft-radius circle on the left, which has area

    1%2F4·p(20)² = 1%2F4·400p square feet = 100p square feet 

3. one quarter of a small 10ft-radius circle on the top, which has area

    1%2F4·p(10)² = 1%2F4·100p square feet = 25p square feet.  

Total = 1875p + 100p + 25p = 2000p square feet of grazing area.

Edwin McCravy aka AnlytcPhil