Posted by **alya** on Saturday, October 15, 2011 at 5:28am.

a piece of wire of length 136(pai) is cut to form 8 circles. the radius of the circles differ from each other, in sequence, by 1 cm.

a) find the radius,r

b) find the number of complete circles that can be formed if the original length of the wire is 190(pai)

- HELP-PROBLEM SOLVING IN MATHEMATICS -
**drwls**, Saturday, October 15, 2011 at 7:02am
How long is a "pai" ? I am not familiar with that unit of length

- HELP-PROBLEM SOLVING IN MATHEMATICS -
**alya**, Saturday, October 15, 2011 at 7:59am
3.142

- HELP-PROBLEM SOLVING IN MATHEMATICS -
**Writeacher**, Saturday, October 15, 2011 at 8:02am
I think you mean *pi*, right?

http://www.google.com/search?rlz=1C1GGGE_enUS379US379&gcx=c&sourceid=chrome&ie=UTF-8&q=pi

- HELP-PROBLEM SOLVING IN MATHEMATICS -
**alya**, Saturday, October 15, 2011 at 9:03am
yup.. pi.. so i want to know how to solve it

- HELP-PROBLEM SOLVING IN MATHEMATICS -
**drwls**, Saturday, October 15, 2011 at 9:12am
pi is the number but what is the dimension? Is the original wire length 136 pi centimeters?

- HELP-PROBLEM SOLVING IN MATHEMATICS -
**Reiny**, Saturday, October 15, 2011 at 9:26am
I agree that you probably meant 136π for the length of the wire

let the first circle have a radius of r

then the others are

r+1, r+2 ,.. , r+7

so the circumferences would be

r(2π) + (r+1)(2π) + ... + (r+7)(2π)

= 2π[ r + r+1 + ... + r+7 ]

= 2π[ 4(r + r+7) , using (n/2)(first + last) as the sum of n terms of an AS

= 2π(8r + 28)

= 136π

2π(8r+28) = 136π

8r + 28 = 68

r = 5

check:

circumferences are

2π(5+6+...+12)

using (n/2)(first + last) as the sum of n terms of an AS

= 2π(4)(5+12) = 136π

length of wire = 136π , perfect!

b)

I assume your circles will start with a radius of 5 and increase by 1

let the number of complete circles be n, where n will have to be a whole number

2π(5 + 6 + .. (n-1) ) = 190π

5+6+... + 5+n-1 = 95

(n/2)(5 + 5+n-1) = 95

n(9+n) = 190

n^2 + 9n - 190 = 0

(n-10)(n+19) = 0

n=10 or a negative

So he will be able to form 10 complete circles.

check:

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