Area of Squares

zee-f · 2012-11-14 12:13:22

Ok sounds good good night ! and thanks

zee-f · 2012-11-15 00:38:14

850

Bob · 2012-11-15 00:44:27

hi zee-f

How did you get that?

Just the 3/4 circle figure on its own comes to much more than that.

Bob

zee-f · 2012-11-15 00:56:07

8500 I counted each square but I forgot to multiply it by ten so it equals= 8500

Bob · 2012-11-15 01:01:52

Ok. That's better. I make it a bit less but it was supposed to be an estimate.

If you look back to the question (post 48), there are lots of steps. If you go through these one at a time I think you can improve that estimate.

Bob

zee-f · 2012-11-15 01:13:39

a bit confused now. The area #6 is asking about is 5890.48622548 right?
3/4 * 50^2 * PI

Bob · 2012-11-15 01:28:35

The question tries to lead you through the steps.

Q6. Just give the goat freedom to move until the rope touches the edge of the barn.

That is the answer you have given.

Q7. What is the new radius when B is the new centre (rope had snagged the corner of the barn at B). And what area this time.

I have colour coded the diagram to make it easier (I hope).

For Q6 look at the yellow area.

For Q7 look at the red area.

zee-f · 2012-11-15 01:53:59

ok the yellow is 3/4 the other area is 1/4 So the area of the whole part of 1/4 = 625PI

zee-f · 2012-11-15 01:56:25

OOOH So now its 30 not 50

zee-f · 2012-11-15 01:57:36

So 657PI is the area

Bob · 2012-11-15 02:55:27

30 is right for the radius and it should be 1/4

657PI ??

What calculation did you do?

Bob

zee-f · 2012-11-15 04:12:51

I did 3/4 3aaaaaa 1/4 * 50^2 * PI= 625PI

zee-f · 2012-11-15 04:15:13

So the area of b is 625 PI

Bob · 2012-11-15 05:49:58

1/4 * 50^2 * PI= 625PI

Wrong radius.

Bob

zee-f · 2012-11-15 08:26:27

1/4 * 30²*PI= 225 PI

Sorry got a little mixed up this problem is confusing even when I get whats happening.

Bob · 2012-11-15 08:50:27

OK. So now for

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?

Now the reverse of the yellow bit is the yellow bit again so that's just Q6 all over again. And don't add it up for the total grass twice as the goat can only eat it once.

So I assume this means wrap the rope around point D and continue with the bit I've shaded green on my diagram. If you have a look you'll see that the red and green bits overlap.

So if you take green as 1/4 30^2 PI again you'll count a bit twice. Roughly how much is the bit in the overlap?

Bob

zee-f · 2012-11-15 09:19:24

about 20 and a half

zee-f · 2012-11-15 09:26:33

but they are the same thing So its going to be 1/4 * 30^2 * PI again right?

Bob · 2012-11-15 09:49:31

See picture

Bob

zee-f · 2012-11-15 09:59:34

so I subtract that bit from the 30

Bob · 2012-11-15 10:02:00

What I thought is

three quarter yellow bit +

red quarter cicrle +

green quarter circle

less the overlap.

So: how much for the overlap ?

Bob

zee-f · 2012-11-15 10:05:24

yup thats what I have in my notes but I thought that was wrong I get 20 and a half like that overlapping area 2 squares and a half

Bob · 2012-11-15 10:07:48

2 squares and a half ???

I'm talking about the black bit

Bob

zee-f · 2012-11-15 10:15:11

OOOh so not that whole overlapping area? the black is one square= 10

Bob · 2012-11-15 10:17:26

It is one square but the area of a square is not 10. We've had this before. How long and wide is a square?

Bob

Math Is Fun Forum

#76 2012-11-14 12:13:22

Re: Area of Squares

#77 2012-11-15 00:38:14

Re: Area of Squares

#78 2012-11-15 00:44:27

Re: Area of Squares

#79 2012-11-15 00:56:07

Re: Area of Squares

#80 2012-11-15 01:01:52

Re: Area of Squares

#81 2012-11-15 01:13:39

Re: Area of Squares

#82 2012-11-15 01:28:35

Re: Area of Squares

#83 2012-11-15 01:53:59

Re: Area of Squares

#84 2012-11-15 01:56:25

Re: Area of Squares

#85 2012-11-15 01:57:36

Re: Area of Squares

#86 2012-11-15 02:55:27

Re: Area of Squares

#87 2012-11-15 04:12:51

Re: Area of Squares

#88 2012-11-15 04:15:13

Re: Area of Squares

#89 2012-11-15 05:49:58

Re: Area of Squares

#90 2012-11-15 08:26:27

Re: Area of Squares

#91 2012-11-15 08:50:27

Re: Area of Squares

#92 2012-11-15 09:19:24

Re: Area of Squares

#93 2012-11-15 09:26:33

Re: Area of Squares

#94 2012-11-15 09:49:31

Re: Area of Squares

#95 2012-11-15 09:59:34

Re: Area of Squares

#96 2012-11-15 10:02:00

Re: Area of Squares

#97 2012-11-15 10:05:24

Re: Area of Squares

#98 2012-11-15 10:07:48

Re: Area of Squares

#99 2012-11-15 10:15:11

Re: Area of Squares

#100 2012-11-15 10:17:26

Re: Area of Squares

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