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Thin wire 40m is cut in 2. A Circle & a sqre.

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 Post subject: Thin wire 40m is cut in 2. A Circle & a sqre.
 Post Posted: Tue May 13, 2008 5:11 pm 
Thin wire is cut in two - a circle and a square. What is the total area in terms of r of both?

Ans: pie r^ + (10 - 1/2 pie r)^2

Can't figure out how to get the square...problem solving must have something to do with the initial '2' pieces, no?
Is it = to 5 separate radius...i.e 2 for the circle and 4 for the square..but 40 is not a multiple of 6..

Any insight most appreciated.
thanks.[/list]
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RonPurewal
 Post subject: Re: Thin wire 40m is cut in 2. A Circle & a sqre.
 Post Posted: Wed May 14, 2008 5:54 am 
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ManhattanGMAT Staff


Posts: 7146
Anonymous wrote:
Thin wire is cut in two - a circle and a square. What is the total area in terms of r of both?

Ans: pie r^ + (10 - 1/2 pie r)^2

Can't figure out how to get the square...problem solving must have something to do with the initial '2' pieces, no?
Is it = to 5 separate radius...i.e 2 for the circle and 4 for the square..but 40 is not a multiple of 6..

Any insight most appreciated.
thanks.[/list]


based on the title of the post, i'll assume that the problem states a total length of 40 for the wire. if this is not the case, kindly post the correct problem statement.

--

in this post, 'p' stands for pi, and i'll assume lengths are in inches

the area of the circle is pr^2. no problems there.

here's the process for figuring the area of the square:
* the circle's circumference is 2pr, which is how much of the wire is used in making the circle
* therefore, there is (40 - 2pr) inches of wire left for the square
* divide by 4 to find that each side of the square measures (10 - pr/2) inches
* so the area of the square is (10 - pr/2)^2 square inches

hth
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