Math Is Fun Forum

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Areas Review

Attached the picture below.

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

6. How much of the 50 foot circle can the goat reach without getting interrupted by the barn? What is that area?

7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

8. When the rope goes around the barn the other way, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

9. 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?

10. What is the total grazing area the goat can reach?

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

Hi;

Check this out:

http://www.mathisfunforum.com/viewtopic … =19992&p=1

Post #3 onwards.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

Hi,

I read the forums but it wasn't very what the final answers were
Could we start by doing number 6 if that's not too much trouble.
The teacher said I have to use the formula for the area of a circle. What is it? And how can I use it?

THanks
Mathew

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

1875 pi was not right?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

I have to show my work, and I don't see the formula anywhere.

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

Hi;

Here is the drawing for 6.

What is the radius of the circle?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

50 feet?

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

That is correct and what is the formula for the area of that whole circle, black and red part combined?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

I think the area of a circle is Area = pi × r^2

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

That is correct. Now do you see the red arc of the circle in the drawing? That is the arc that the goat can make with his 50 ft leash. What is the area of that?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

area = pi * r^2
area = pi * 50^2

Is this correct till now?

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

Yes that is the area of the whole circle. We are interested in the red area. Cab you get that?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

The red area is 3/4 of the whole circle, how can i incorperate that in the equation?

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

For instance, what is (3 / 4) of 100?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

75 is the 3/4 of 100

Okay I think almost I got it.

If the area = pi * 50^2
area = 7853.98
I have to get 3/4 of 7853.98

How can I do that?

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

The same way you got (3/4) of 100. You multiply them.

(3/4) * 100 = 75

(3/4) * pi * 50^2 = ?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

That was the answer: 5890.485

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

Yes or 1875 pi.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

Okay now how about number 7?

7. When the rope goes around the barn, what is the new radius? How much of a circle can it make without hitting the barn or overlapping area you've already found? What is that area?

---

I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

The new radius is 30.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

Can you show your work, because the teacher will want it. But thanks!!!

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

The area is the area in red. How much do you think that is?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

It is 1/4 of the total area.

(1/4) * pi * 50^2 = 1963.495 (how much is that in pi)

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

rogerwaters

Member

Registered: 2013-11-02

Posts: 85

Re: Areas Review

So that is my answer for number 7 right?

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I think there are things in my story that have helped my creativity. Your father being killed, for instance, is one of the best things that could happen to a kid if he's going to write poetry or songs.
-Roger Waters

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Areas Review

Nope, the radius is only 30. 20 feet got used up by the wall of the barn.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.