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: Find the radius!  ( 5892 )
« : September 22, 2007, 12:11:27 AM From Shrinidhi»



Find the radius!


You are given 2 coins and a pencil. One coin is bigger, with an unknown radius R. The other coin is smaller with a radius r=5 mm. Given that R is an integral multiple of r, find the unknown radius R, using no other resources than provided.

 
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« #1 : September 25, 2007, 07:54:45 PM From Sudeep»

Method 1:
Take the bigger coin of radius R.. Draw a circle using this coin with the pencil.

Now take the small coin of radius 5mm and draw the circles using it along the circumference on the inside of the bigger circle approximately in one of the semicircles. keep filling it such that the smaller circles touch eachother but not overlap...

stop the above process untill it reaches the  center...

u ve the radius from the count of the small circles along the diameter of the bigger circle.

Method 2:
if v r allowed to draw the diameter... it becomes more simple. just adjust the smaller coin along the diameter with the center on the diameter.

To draw the diameter v can simply draw the circle of the biggger coin.. and then fold the paper such that the semicircles.. coincide.

But.. there might be a shorter one??

Sorry i am bad at explaining thngs :'(
« #2 : September 25, 2007, 09:25:24 PM From Shrinidhi»

Sudeep, Method 2 is not practical as you cannot draw the diameter using the resources provided. Method 1 will also not be accurate as you cannot ensure that the smaller circle diameters form a straight line. However, one might get the solution by following Method 2 if the value of R is small as it is an integral multiple of r.

Better solution, anyone?
« #3 : September 25, 2007, 11:20:16 PM From gvarun_1»

keep the bigger coin at a place and hold it firmly. mark a reference point A on the circumference of the bigger coin. take the small coin with known radius and mark a reference point B on it. place the smaller coin adjacent to the bigger one such that both the points coincide and start rotating the smaller coin along the circumference of the bigger coin until we get back to the reference point A and also as R is an integral multiple of r, after such an exercise both A and B should be coinciding. We note down the number of rotations of the smaller coin we made around the bigger circle (say n) and that many times r would give the value of R.
2*pi*R= n*(2*pi*r)
=> R=nr
hope i explained as i intended to explain :)
« #4 : September 26, 2007, 10:21:38 PM From spazinvader»

Well i got a method which i think wont be a better one.But may help others.

1)keep the 'R' radius coin down and draw a circle
2)From any of the border,start drawing the circle of 5mm coin.
Both of them should have one of their at least touched.
3)Draw from the other side of the circle
Like drawing it in the direct other side
4)Keep the inner circle as the border and draw another circle like done in step 2
That is,a 5mm circle should be drawn by keeping the fore drawn circle as border and make sure that they just touch themselves.They should not overlap.
5)Repeat it continuously until you reach the circle drawn in the second step.
Since it is an integral multiple of 5,it's diameter will be divisible by 10 itself.So we will get the borders touching if we have drawn correctly the circles through diagonal.
Now if there are "N" number of circles there,then the radius will be 5*N/2.

Any comments?Am i wrong any where?Or totally wrong?
« #5 : October 02, 2007, 01:38:15 PM From Rajesh»

if bigger coin is kept fixed and we rotate the smaller coin on outer surface of bigger one (assuming there is enough friction so that both the coins will not slide)....and if n is number of rotations the smaller coin has completed on outer surface of bigger coin to complete one journey on it....

so....     n = R/r + 1
hence    R = r(n-1)
               =5(n-1) mm
« #6 : October 03, 2007, 05:03:37 PM From menezesjackson»

keep the unknown rad coin firm....
rotate the smaller around it....
now count the total no of rotations it takes.....
subtract 1 by that.....
multiply by 5..... :)


if u do the exp u understand the subtraction of 1
« #7 : October 09, 2007, 07:41:39 PM From Shrinidhi»

Everyone is conceptually right. But equation is wrong. Why subtract 1 from the number of rotations?

The solution I was thinking of was...

Circumference of the circle with radius r * number of rotations of the smaller circle around the bigger one =  circumference of the circle with radius R.

2*Pi*5 * n = 2*Pi*R

5n = R.

R = 5n.
« #8 : October 11, 2007, 03:54:12 PM From Rajesh»

@ Srinidhi...
Go through the links...n i hope..u will understand that....!!

http://www.cut-the-knot.org/pythagoras/two_coins.shtml
http://www.jimloy.com/puzz/coin.htm
« #9 : October 12, 2007, 02:37:47 PM From spazinvader»

You are right shrindhi.
I have taken as diameter instead of radius.
Thanks for that.
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