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

You are not logged in.

- Topics: Active | Unanswered

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,002

Correct!!

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

3- 11.25/360 * pi* 10²= 25/8PI

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: 7,002

That's correct too!

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

#4- What would the area of the whole pizza be if it were made of half pieces?

does't that mean the same original pizza but with 32 pieces ?

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: 7,002

Yes but it would still have the same area.

See my picture.

I think it means what would the area be of a 16 piece pizza with all the pieces half the size of the original.

So what is the yellow area?

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

my teacher said:

You should take the problem literally. What would the area of the "whole pizza be?"

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

So the same area 100 pi is the answer right?

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,002

OK. That would be right. I'm glad you checked.

Bob

Offline

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

Oh OK so even if they were in half the area stays the same 100 pi .

Thanks Bob

*Last edited by zee-f (2012-11-12 01:23:19)*

Offline

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

5. What is the radius of a half-piece? (ie, where do I need to cut to make two equal halves out of a piece?)

5- The radius stays the same 10 inches.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,002

No, I disagree. This time I'm confident about what the question is asking.

On my diagram you need to find the yellow circle radius if yellow area = red area = half original pizza.

Bob

Offline

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

OOOh So the radius would be 5 .

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,002

No again. You want the area to be half. dividing the radius won't do that.

eg A 10 by 10 square has an area of 100

A 5 by 5 square has an area of 25.

You have to half the area then work backwards from

Bob

Offline

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

area= 100PI/2 = 50PI

radius= 50PI ÷ 2 = 25PI

Offline

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

square root of 25PI is 5PI

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,002

When you have a two stage formula and you want to 'un-do' it, you need to do the inverse steps in the reverse order.

means you start with the radius, then square it, then times by pi.

So to go from area to radius you need to

start with the area, divide by pi, then square root the answer.

see diagram.

Bob

Offline

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

ok so half the area of 100PI=50 PI

50PI ÷ PI = 50

√50 = 5√2 = Radius

so the area is 50 PI

Offline

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

then when I do the opposite

5^2√2 ^2* PI = 50 PI

*Last edited by zee-f (2012-11-12 03:04:22)*

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,002

hi zee-f

5^2√2 ^2* PI = 50 PI

I think you have got it but it is unclear here what you are saying the radius is.

Please state R = ??

Bob

Offline

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

R=5√2

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,002

That's what I was waiting for. Excellent!!

Bob

Offline

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

Thank you sooooooooooooo much

Offline

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

Ok I have 5 more to go but I cant picture it or draw it it's so confusing

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?

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,002

hi zee-f

I've had a go at what I think this begins to look like.

I haven't done it all. I think you need to add some thinking to the diagram too.

I started with a rectangle to represent the barn and labelled it ABCD.

And I decided to fix the rope at corner A.

My scale is one square represents 10 feet.

As the goat moves about some grass is freely available to it. It cannot reached further out than the rope will allow so I made a circle based on that radius.

It seems to me that from E round to F and G right round to H there's no problem with the rope and the barn.

This is what my first diagram shows. Area that the goat can reach shaded yellow.

But if the goat tries to go beyond point H part of the rope snags against the side of the barn and so corner B acts as a new centre. 20 feet of the rope is locked against the side of the barn AB, so the circle of access is reduced to 30 feet centred on B

Diagram 2 shows the area the goat can reached from H to I.

Then the rope gets snagged again at side BC.

So what do you think happens next?

Bob

Offline

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

I am still confused so the base of the rectangular barn is 50 and the height is 20? the goat is tied in the (A) corner (of the circle u drew )

Offline