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# 40 meters wire problem

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40 meters wire problem [#permalink]  15 Jun 2009, 00:35
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A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius R, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and square regions in terms of R.

1) \pi R^2
2) \pi R^2 + 10
3) \pi R^2 + 1/4\pi^2R^2
4) \pi R^2 + (40 - 2\pi R)^2
5) \pi R^2 + (10 - 1/2\pi R)^2

4) or 5) is a given, I just dont see how you make the calculation necessary.
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Re: 40 meters wire problem [#permalink]  15 Jun 2009, 01:15
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Given:
40 meters long wire cut into two pieces.

Now Length of piece one = circumference of a circle with radius R = 2\pi R

Length of piece two = perimeter of a square created using the remaining wire = 40-2\pi R

\Rightarrow \text{length of each side of square} = \frac{40-2\pi R}{4}

= \frac{4(10-\frac{1}{2}\pi R)}{4}

= 10-\frac{1}{2}\pi R

Now
\text{Area of circle} = \pi R^2
\text {Area of square} = (10-\frac{1}{2}\pi R)^2

\text {Sum of the areas}=\pi R^2 + (10-\frac{1}{2}\pi R)^2
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Re: 40 meters wire problem [#permalink]  15 Jun 2009, 03:01
Option 'E' is correct.
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Re: 40 meters wire problem [#permalink]  07 Jan 2012, 11:49
GREAT EXPLANATION NOOKWAY. THANK YOU
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Re: 40 meters wire problem   [#permalink] 07 Jan 2012, 11:49
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