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

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Senior Manager
Joined: 27 Aug 2005
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A thin piece of wire 40 meters long is cut into two pieces. [#permalink]  22 Sep 2005, 19:09
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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. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

A. Pi*(r)^2
B. Pi*(r)^2 + 10
C. Pi*(r)^2 + 1/4*(Pi)^2*(r)^2
D. Pi*(r)^2 + (40-2*Pi*r)^2
E. Pi*(r)^2 + (10-1/2*Pi*r)^2
Senior Manager
Joined: 03 Nov 2004
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E here. since the wire = 40 when cust into 2 pieces one piece is circle with A=pr^2 . the square is a bit tricky since we have to take 1/4th of the remaining part of the wire after we have used the other for the radius of the Circle. 1/4th of the remainder is the side of the square - the side is equal to 10 - 1/2*P*r and the area is [10 - 1/2*P*r] ^2 therefore answer E.
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Re: PS: Circle and Square [#permalink]  22 Sep 2005, 20:42
1. the first piece = the lenth of the perimeter of the circle = 2(pi)r.
area of the circle = (pi)r^2

2. second piece = total length - perimeter of the circle = 40-2(pi)r.
a side of the square = 1/4 of 40-2(pi)r = 10-(1/2) (pi)r
area of the square = [10-(1/2) (pi)r]^2

so the desired are = (pi)r^2 + [10-(1/2) (pi)r]^2, which is E.
Senior Manager
Joined: 22 Jun 2005
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Area of cirlce: pi*r^2

Area of square: ((40 - pi*2*r)/4)^2

the latter can be simplified to (10 - pi*r/2)^2
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