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

Algebra.Com
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)   (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)   (Show Source): You can put this solution on YOUR website!
That's wrong. Check this site later.
Answer by AnlytcPhil(1806)   (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

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

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

    ·p(20)² = ·400p square feet = 100p square feet 

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

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

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

Edwin McCravy aka AnlytcPhil
RELATED QUESTIONS

I really need help understanding how to work this word problem out. If there is a goat (answered by edjones)
If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet... (answered by stanbon)
If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet... (answered by stanbon)
A square barn measures 14 meters on each side. A goat is tethered outside by a rope that... (answered by Theo)
A goat is tied to a corner of a 60 ft. by 75 ft. barn in the center of a grassy field.... (answered by josgarithmetic)
A square barn measures 42 ft on each side. A goat is tethered outside by a rope that is... (answered by kiru_khandelwal)
Find the total grazing area of a goat G, The animal is tied to a corner of a 40'x40'... (answered by ankor@dixie-net.com)
Find the total grazing area of the goat G represented in the figure (a top view) shown at (answered by Alan3354,ikleyn)
Could you please help me with this problem? Would greatly appreciate it! A cow is tied (answered by ankor@dixie-net.com)