Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

Ok sounds good good night ! and thanks

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

850

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

hi zee-f

How did you get that?

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

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

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

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

a bit confused now. The area #6 is asking about is 5890.48622548 right?

3/4 * 50^2 * PI

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

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.

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

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

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

OOOH So now its 30 not 50

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

So 657PI is the area

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

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

657PI ??

What calculation did you do?

Bob

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

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

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

So the area of b is 625 PI

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

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

Wrong radius.

Bob

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

1/4 * 30²*PI= 225 PI

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

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

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

about 20 and a half

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

See picture

Bob

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

so I subtract that bit from the 30

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

What I thought is

three quarter yellow bit +

red quarter cicrle +

green quarter circle

less the overlap.

So: how much for the overlap ?

Bob

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

2 squares and a half ???

I'm talking about the black bit

Bob

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

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

Offline