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# A thin piece of wire 40 meters long is cut into two pieces.

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A thin piece of wire 40 meters long is cut into two pieces. [#permalink]  21 Jul 2008, 08:16
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 the square regions in terms of r?

Πr^2

(Πr^2) +10

Πr^2 + (1/4)(Π^2)(r^2)

Πr^2 + (40-2Πr)^2

Πr^2 + (10-.5Πr^2)^2

(Just so you know, Π = pi)
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Re: Cuttin' Wire [#permalink]  21 Jul 2008, 08:25
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Expert's post
ryguy904 wrote:
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 the square regions in terms of r?

We make a circle with radius r: the area is Pi*r^2.

How much wire is left? The wire we used for the circle is equal to the circumference of the circle: 2r*Pi. We have 40 - 2r*Pi meters of wire with which to make the square. Thus, 40 - 2r*Pi will be the perimeter of the square, and each side will be one quarter that length: 10 - 0.5r*Pi. The area of the square will be (10 - 0.5r*Pi)^2, and if you add that to Pi*r^2, you'll get the answer.
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GMAT Tutor
Joined: 24 Jun 2008
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Kudos [?]: 947 [0], given: 4

Re: Cuttin' Wire [#permalink]  21 Jul 2008, 08:29
Expert's post
ryguy904 wrote:
Πr^2 + (10-.5Πr^2)^2

I think you must have mistyped this answer choice- it would be the correct answer if r were not squared. That is, it should read:

Πr^2 + (10-.5Πr)^2
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Current Student
Joined: 27 Jul 2007
Posts: 873
Location: Sunny So Cal
Schools: CBS, Cornell, Duke, Ross, Darden
Followers: 12

Kudos [?]: 191 [0], given: 4

Re: Cuttin' Wire [#permalink]  21 Jul 2008, 08:34
IanStewart wrote:
ryguy904 wrote:
Πr^2 + (10-.5Πr^2)^2

I think you must have mistyped this answer choice- it would be the correct answer if r were not squared. That is, it should read:

Πr^2 + (10-.5Πr)^2

You are correct. I got a little trigger happy typing in the ^2's. LOL

+1 Thank you so much. I couldn't understand the square's area, but you explained that I was simply deducting the perimeter.

Cheers
Re: Cuttin' Wire   [#permalink] 21 Jul 2008, 08:34
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