What area of grass can the goat eat?

[chijioke]

A goat is tied to a peg in the ground. The rope is 3 m long. What area of the grass can the goat eat?
How do I solve this problem? I know that if the rope is used to form a circle, the perimeter would be [math]2 \pi r = 2~m[/math] Maybe from there I can get the radius r which I am thinking I can use to find the area of the rope which is used to form a circle. But even I find such area will the area be equal to the area of grass the goat can graze? How do I go about this problem?

 

[Dr.Peterson]

A goat is tied to a peg in the ground. The rope is 3 m long. What area of the grass can the goat eat?
How do I solve this problem? I know that if the rope is used to form a circle, the perimeter would be [math]2 \pi r = 2~m[/math] Maybe from there I can get the radius r which I am thinking I can use to find the area of the rope which is used to form a circle. But even I find such area will the area be equal to the area of grass the goat can graze? How do I go about this problem?

You seem to be totally misinterpreting the problem. The rope does not form a circle; it ties the goat to the peg.

So you are told the radius of the region it can eat: 3 meters. That's because it can eat anything within that distance of the peg.

 

[khansaheb]

A goat is tied to a peg in the ground. The rope is 3 m long. What area of the grass can the goat eat?
How do I solve this problem? I know that if the rope is used to form a circle, the perimeter would be [math]2 \pi r = 2~m[/math] Maybe from there I can get the radius r which I am thinking I can use to find the area of the rope which is used to form a circle. But even I find such area will the area be equal to the area of grass the goat can graze? How do I go about this problem?

Please post a copy of the original problem, as it was presented to you - including any relevant figure.

 

[The Highlander]

A goat is tied to a peg in the ground. The rope is 3 m long. What area of the grass can the goat eat?
How do I solve this problem? I know that if the rope is used to form a circle, the perimeter would be [math]2 \pi r = 2~m[/math] Maybe from there I can get the radius r which I am thinking I can use to find the area of the rope which is used to form a circle. But even I find such area will the area be equal to the area of grass the goat can graze? How do I go about this problem?

Does this help???

​

Please draw and show us your own sketches in future!

 

[khansaheb]

Does this help???

View attachment 35673​

Please draw and show us your own sketches in future!

But I suspect there is a fence or a wall - and that would make the problem a bit more interesting.

 

[The Highlander]

But I suspect there is a fence or a wall - and that would make the problem a bit more interesting.

Anything is possible, of course, but experience of this OP suggests that the problem is just as simple as @Dr.Peterson and I have interpreted it. ?‍

 

[khansaheb]

Anything is possible, of course, but experience of this OP suggests that the problem is just as simple as @Dr.Peterson and I have interpreted it. ?‍

We have seen example of your simple interpretation !!

riddle - clock hands

How many times the minutes hand is on the hours hand in 24 hours in analog clock?

www.freemathhelp.com

 

[chijioke]

Does this help???

View attachment 35673​

Please draw and show us your own sketches in future!

Interesting! That means the goat is standing at the circumference of an imaginary circle. How do we interpret that?

 

[Dr.Peterson]

Interesting! That means the goat is standing at the circumference of an imaginary circle. How do we interpret that?

Please tell us how you interpret the problem! And if you didn't state the entire problem (so that it is in fact more complicated than we think), please do.

The goat in the picture is in one of the many places (in green) that it can get to; the circumference of the circle is as far as it can get.

Here is a discussion of two of the more interesting problems of this sort:

Goat grazing problem - Wikipedia

en.wikipedia.org

Here is another:

A goat tied to a rectangular barn - Math Central

 

[chijioke]

Please tell us how you interpret the problem! And if you didn't state the entire problem (so that it is in fact more complicated than we think), please do.

That is how I interpreted the problem. But I have seen that your interpretation

View attachment 35673​

is the best because the goat can't move far beyond the arc of the circle which radius (length of rope) defines size of circle. The goat can only graze the area of
the circle. Thanks for that wonderful diagram.
So going by the diagram, the area of the grass the goat can graze is [math]\pi r^2= 3.1×3^2=27.9~m^2[/math]

 

[The Highlander]

View attachment 35690
View attachment 35689 That is how I interpreted the problem. But I have seen that your interpretation
is the best because the goat can't move far beyond the arc of the circle which radius (length of rope) defines size of circle. The goat can only graze the area of
the circle. Thanks for that wonderful diagram.
So going by the diagram, the area of the grass the goat can graze is \(\displaystyle \pi r^2= 3.1×3^2=27.9~m^2\)

I just had to smile at your attempt at a sketch. ?

 

[chijioke]

I just had to smile at your attempt at a sketch. ?

Thanks for smiling. Smiling makes one look younger.