moose!
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(17:58 on Mon 20/Dec/04)
Bizarre but after scribbling on a piece of paper it seems its true.
Circumference = 2 X PI X radius
So with poles = 2 X PI X (radius + 6)
= (2 X PI X radius) + (2 X PI X 6)
= (2 X PI X radius) + (2 X 3-ish X 6)
= (Original value) + 36
So I guess I make it 36 feet but still not much extra!
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moose!
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(18:06 on Mon 20/Dec/04)
I guess you can compare this with putting a string around a beach ball. To make a gap of a just a single millimeter around the beach ball wouldn't really need any noticeable increase in the amout of string. So, in comparison, 6 feet isn't really much compared with the Earth's radius of 6000km.
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bernardo
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(18:09 on Mon 20/Dec/04)
It would have to be 2 pi 6 feet longer, which is 12 pi which is about 38 feet.
This question is usually quoted as being a rope which is 6 feet longer, and which can be lifted almost a foot above the ground.
The circumference of a circle is 2 pi r, not pi r.
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bernardo
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(18:11 on Mon 20/Dec/04)
by the way, the thing which "dictates" to you that it "must have to be" longer is not logic, but instinct. This is where maths and logic are different from intuition and instinct.
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bernardo
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(18:14 on Mon 20/Dec/04)
I have just realised that moose!'s answer is confused. The amount of length that you need to increase the rope in order to produce an extra 6 feet of radius is 38 feet, regardless of how big the Earth is. An extra 38 feet of length in a string round a beach ball (or a grain of sand, or the sun, or a ferris wheel) would produce an extra 6 feet of radius in all cases.
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newtron
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(18:18 on Mon 20/Dec/04)
Yep, Bernardo's right. That's the whole point of the problem. The original radius "r" cancels out.
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moose!
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(18:19 on Mon 20/Dec/04)
I realise that bernado, I was just trying to give a non-mathematical answer why such a small amount extra is required.
I don't think anyone would be surprised if you needed a lot of extra rope if you but 6-foot poles on a beach ball, now would they!
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magicdice
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(15:43 on Fri 24/Dec/04)
Anyone got any better ideas than just relying on a mathematical formula?
*chokes on her fruit juice* just mathematics?!
sweetie if we didn't exist, there'd be no human logic, no instinct, no intuition. but zero would still exist, the formula for the circumference of a circle would be the same... mathematics is the one true thing in life that you genuinely can trust because it is unaffected by us: we don't theorise, experiment, invent, we discover mathematics. it's more true than anything you can possibly imagine
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Kingaroo
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(18:42 on Wed 29/Dec/04)
"Pi r squared" is the AREA of a circle, not the circumference.
You can remember this because the answer is in SQUARE feet :(or whatever unit)
"2 pi r" (the correct formula for circumference) is also the same as "pi d" (D = diameter, which is twice the radius)
If you remember "pi D", you won't get confused by the number 2 being in both formulae.
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PatTheRat
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(18:04 on Wed 05/Jan/05)
One little thing all you guys are forgetting here...2.pi.r is the formula for calculating the circumfrence of a circle, a perfect circle. Now correct me if I'm wrong, but i dont believe the earth is a perfect round shape. Hence 2.pi.r is too general to be used.
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magicdice
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(00:20 on Sun 09/Jan/05)
PatTheRat you are correct, it's what is known as an oblate spheroid (i.e. it's a sphere that's slightly squished at the poles) however it's close enough to suffice for a theoretical discussion such as this, and the earth is just being used here as an illustrative device - it's not actually about the equator of the earth but about circumferences
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georgeous
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(19:22 on Sun 23/Jan/05)
if you added another 6 ft to the radius of the Earth then the circumference would only be 1.915 metres longer to be precise
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georgeous
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(19:23 on Sun 23/Jan/05)
sorry 1.9151
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landie
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(19:17 on Thu 12/May/05)
I think you're mixed up gorgeous, the amount of 6ft and 1.9m (1.8288 metres actually) are the same thing. You wold need to multiply by 2 pi r to find the circumference, as others have rightly said.
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Hamish
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(09:32 on Wed 10/Aug/05)
A non-mathamatical answer .... and experiment!
Draw a scale diagram of the earth and measure its circumfrence - ass the poles and draw in the rope - re measure the circumfrence. work out the differance (sorry maths here, but only arithmatic). Multiply by scaling facor - I think you will find the answer is quite small.
Note; 2pi r = pi d = circunfrence of circle
pi r^2 area of circle
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jimmydean
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(22:18 on Wed 22/Feb/06)
An extra 38 feet of length in a string round a beach ball (or a grain of sand, or the sun, or a ferris wheel) would produce an extra 6 feet of radius in all cases.
Sorry but if you think about it.. this definatly isnt true.. If you had a beach ball with a 6 foot pole on it, you wouldnt need 38 feet of rope to go around it.. thats just redicilous.
You are treating the problem as if you are still working with a sphere, however you are not. when you add the 6 foot pole to the sphere you just changed the shape of the sphere to something else, and therefore the problem becomes more complex. there isnt just a simple solution to it.
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