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simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

This circles question set that is the bane of my existence right now

I'm having a lot of trouble with this question -- my mom completely lost her cool with me because I just couldn't get my head around it! So now I'm on my own until I can solve it, which I can't, because I'm very much trash at math.

A farmer ties a horse to a building on a 50 foot lead.   The building measures 20 feet by 20 feet (floor).  What is the maximum area the horse can use for grazing? If there are regions you can't find the area of, provide as good an estimate as you can. Assume the horse is tied to a corner outside the building, cannot get in, and that the building is not grazing area. (Remember, this will be based on parts of circles, no other shapes...the horse's rope will only get shorter when he tries to go around the building...)

https://i.imgur.com/w0x2mU4.png

1. How much of the 50-foot circle can the horse reach without getting interrupted by the building? What is that area?
A: So, since the radius (the lead) is 50, the area of the whole circle is 7853.98? And since it's only the 50-foot circle, I gotta remove the quarter part, 7853.98/4 = 1963.495, so 7853.98 - 1963.495??? I'm dying. 5890.485. Is that it? Surely not.

2. Assume the horse has grazed all of the grass in the area covered by #1 and continues on around the building.  What is the new radius when the rope is interrupted by the building? What is that area covered using this new radius of rope before the rope is interrupted by the building again?
A: Ok, I have no idea. This might as well be Greek because that's as much sense as it makes to me. Can someone please explain how this works to me? What do they mean by the radius when the rope is interrupted? I can't wrap my dumb head around this at all. 'Course, I have no idea about the rest of the questions either.

3. What if the horse had gone around the building the other way.  What would the new radius have been when the rope was interrupted by the building?  What is that area covered using this new radius of rope before the rope is interrupted by the building again?

4. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?

5. What is the total area the horse can graze using your calculations from #1-4?

Thanks a bunch!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: This circles question set that is the bane of my existence right now

hi simonmagusflies

Over the years that I have been helping members this question has come up three times.  It was a goat to start with.  Don't know why it has become a horse.

Here's my diagram for the problem:

The squares are 10 feet by 10 feet.

The building is in white.  The horse is attached at A.   The building is ABCD but I've left off the other letters to keep the diagarm uncluttered. The yellow region can be reached without the rope snagging the building.  Seems you have that bit sorted.

When the horse walks so that the rope lies along AH, it can only reach around the corner by having the rope snag at B.  So B becomes the new centre for getting more grass and the radius is less; you need to subtract AB from the rope length to get the new radius.  The red area can now be calculated.

If the horse goes the other way around the building then a simliar calculation will give you the green area.

But the black bit forms part of both the red answer, and the green answer so you've ended up counting it twice.  There are advanced techniques for calculating it exactly, but they're beyond the level of the module so the question asks you to estimate it.

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob