Note: only basic mathematics is needed.A string is wound symmetrically around a circular rod. The string goes exactly four times around the rod. The circumference of the rod is 4cm and its length is 12cm. Find the length of the string.
Find the length of the string
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Find the length of the string
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Best wishes,
Hans
Hans
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- gamma jay
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Re: Find the length of the string
Tip: If you go to the loo and unwind the inner cylinder of a standard toilet paper roll, and add 4 cm to its length, you'll almost be there.
(Now when the lounge becomes quiet, we'll all know where the members are!!)
(Now when the lounge becomes quiet, we'll all know where the members are!!)
Regards,
Rudi
If your absence does not affect them, your presence didn't matter.
Rudi
If your absence does not affect them, your presence didn't matter.
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Re: Find the length of the string
Spoiler
If you cut the roll lengthwise then you will see the thread making lines across a rectangle. There are 4 lines, each of which is the hypotenuse of a 4x3x5 right angle triangle, so the total length is 5cm * 4 = 20cm
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StuartR
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Re: Find the length of the string
You guys and your math(s)!! Way to clever for me!
Regards,
Rudi
If your absence does not affect them, your presence didn't matter.
Rudi
If your absence does not affect them, your presence didn't matter.
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- BronzeLounger
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Re: Find the length of the string
Very clever!
Regards,
Paul
The pessimist complains about the wind. The optimist expects it to change. The realist adjusts his sails.
Paul
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- gamma jay
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Re: Find the length of the string
Question:
Spoiler
Out of interest, if you could not cut the roll to make it flat, would there be a clever way to work it out using pi or circumference or something like that, even though it might be a bit more complex than the request for a basic solution?
Some interesting formulas here:
- Lenth of line around an object
- Calculating Total Length of Wraps Around A Cylinder
Some interesting formulas here:
- Lenth of line around an object
- Calculating Total Length of Wraps Around A Cylinder
Regards,
Rudi
If your absence does not affect them, your presence didn't matter.
Rudi
If your absence does not affect them, your presence didn't matter.
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Re: Find the length of the string
Spoiler
I don't think a more complicated calculation would help.
You don't even have to cut the cylinder open. In your imagination, apply some ink to the string, then roll the cylinder over a sheet of paper. You'll basically get Stuart's diagram. After four complete revolutions, you'll have a straight line representing the entire string.
You don't even have to cut the cylinder open. In your imagination, apply some ink to the string, then roll the cylinder over a sheet of paper. You'll basically get Stuart's diagram. After four complete revolutions, you'll have a straight line representing the entire string.
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Best wishes,
Hans
Hans
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- BronzeLounger
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Re: Find the length of the string
Spoiler
As soon as I saw the 4 (circumference) and the 12cm/4 turns = 3, I knew a 3-4-5 triangle would appear somewhere. Sure enough it did.