SOLUTION: A cow is tied up to the long side of a barn 10 feet away from the corner. The rope being tied to the barn is 21 feet long. the barn is 11 feet wide and 28 feet long. what is the to
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Question 253024: A cow is tied up to the long side of a barn 10 feet away from the corner. The rope being tied to the barn is 21 feet long. the barn is 11 feet wide and 28 feet long. what is the total area of the space in which the cow may graze.
hello. please if you answer this explain it because i think ill be having to do these questions alot.
thank you Found 2 solutions by Alan3354, ankor@dixie-net.com:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! There's half a circle of radius 21 ft.
1/4 of a circle rad = 3 ft
1/4 of a circle rad = 11 ft
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Area = pi*(21^2/2 + 3^2/4 + 11^2/4)
= (pi/4)*(442 + 9 + 121)
= (pi/4)*572
= 143pi
=~ 449.25 sq feet
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I'll send a sketch if you email via the thank you note.
You can put this solution on YOUR website! A cow is tied up to the long side of a barn 10 feet away from the corner.
The rope being tied to the barn is 21 feet long. the barn is 11 feet wide and 28 feet long.
what is the total area of the space in which the cow may graze.
:
I would suggest that you draw this out more or less to scale. A rectangle labeled
28' by 11'. Place the tie-up point 10 ft from the right end.
Portions of three different sized circles will be apparent as you visualize the
21 ft rope going around the tie-point; the 21'radius being affected by the barn
:
On left side of the barn the rope will exceed the left end of the barn by 3 ft
(28-10) + 21 = 3'
Find the area of 1/4 circle with a 3' radius
A = .25*pi*3^2
A = 7.1 sq/ft
:
A half circle with a radius of 21'
A = .5*pi*21^2
A = 692.7 sq/ft
:
The rope will go around the right end of the barn to the corner exactly
21-10 = 11'
A 1/4 circle with a radius of 11'
A = .25*pi*11^2
A = 95 sq/ft
:
Total area = 7.1 + 692.7 + 95 = 794.8 ~ 795 sq/ft of grazing area
:
Hope this made sense to you. (Study your diagram of the barn and it will)
