Can someone help me set this up??

H

Hard2Do

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Joined
Mar 30, 2006
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5
I have most of the circle; except where the rope gets smaller

Okay here is the question:

A cow is tethered to one corner of a square barn, 10ft x 10ft, with a rope 100ft long.
What is the maximum grazing area for the cow??

i know the answer is 31,145.15 sq ft
but i can not figure out how they got that

Please help
 
Have you tried drawing a circle on each corner of the barn?

Pick a corner for the rope to be tied.
100 ft on the first corner.
90 ft on the adjacent corners.
80 ft on the opposite corner.
Don't forget to subtract the barn.
 
I did that and I have A side side side triangle so i use the law of cosines to get angle A and B but for some reason I get 0 for an angle
 
Since only you can see your drawing, that's a bit tough to follow. What are the sides of your triangle? I'm guessing it's either:

10 ft * 90 ft * 82.65072441 ft

OR

10*sqrt(2) ft * 90 ft * 90 ft.

If it's either of those, whinch angles are you talking about?

You have this piece already? \(\displaystyle \frac{3}{4}*\pi*(100 ft)^{2}\). Good.

Note: There are several useful ways to set this up and get the unique correct answer.

Note: You do not have to draw the 80 ft circle on the opposite corner. I like to throw it in just to demonstrate that it isn't necessary.
 
Hard2Do said:
I have most of the circle; except where the rope gets smaller

Okay here is the question:

A cow is tethered to one corner of a square barn, 10ft x 10ft, with a rope 100ft long.
What is the maximum grazing area for the cow??

i know the answer is 31,145.15 sq ft
but i can not figure out how they got that

Please help

Picture the barn with corners A, B, C and D.
Code: 
A----------------B
*                *
*                *
*                *
*                *
*                *
*                *
-----------------*
D                  C

With the rope tied to corner B:
Assume the rope is lined up with side AB of the barn.
Sweep out a 3/4 circle of 100 ft. radius until the rope coincides with sideBC.
The area swept out is .75(100^2)3.14.
With the rope now fixed at corner C, it now sweeps out a 1/4 circle area of .25(90^2)3.14 until the rope coincides with side CD.
With the rope now fixed at corner D, it now sweeps out a 1/4 circle area of .25(80^2)3.14 until the rope coincides with side DA.

You will now note that, due to overlapping areas, you will have to subtract some area which I will let you figure out.
Click to expand...
 
I am working on adding the picture to a message so you can see what I am talking about
 
pka I have most of that but they don't relay to mine because my cow is teahtered at a corner not in the middle of the barn and the first one is close but it has no barn
 
Hard2Do said:
pka I have most of that but they don't relay to mine because my cow is teahtered at a corner not in the middle of the barn and the first one is close but it has no barn
Click to expand...

What? :shock:
 
Hard2Do said:
okay here is the picture
Click to expand...
Very good, except for one thing. 80 ft is not labeled correctly. The piece you have should be 82.65072441 ft. I told you the 80 ft circle was unnecessary. ;-)

If you connect the two 90-corners of the barn, you will have an isosceles triangle that is much easier to deal with than your concave quadrilateral. You can then subtract the little piece of the barn that you just included.
 
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