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

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Manager
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A thin piece of wire 40 meters long is cut into two pieces. [#permalink]  12 Oct 2008, 21:22
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?
a. pi r^2
b.pi r^2 +10
c. pi r^2 + (1/4) (pi^2)(r^2)
d. Pi r^2 + (40-2pir)^2
e. pi r^2 + (10 - (1/2)pi r)^2
SVP
Joined: 17 Jun 2008
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Re: wire [#permalink]  13 Oct 2008, 04:25
D.

Perimeter of circle = 2pir

perimeter of squre = 40 - 2pir

Total area = pir^2 + (40-2pir)/2
Senior Manager
Joined: 21 Apr 2008
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Re: wire [#permalink]  13 Oct 2008, 04:29
D

Wire = x + (40-x)
x = 2 pi r

area = pi r^2 + (40-2 pi r)^2
Intern
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Re: wire [#permalink]  13 Oct 2008, 14:06
e.

Circumference of circle = 2pir
perimeter of square = 40 - 2pir
length of one side of square = (1/4)(40 - 2pir) = 10 - (1/2)pir
area of square = [10 - (1/2)pir]^2

Total area = pir^2 + [10 - (1/2)pir]^2
Senior Manager
Joined: 21 Apr 2008
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Location: Motortown
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Re: wire [#permalink]  13 Oct 2008, 15:15
Oops found my mistake

Side of the square = (40-2 pi r)/4

E it is
Re: wire   [#permalink] 13 Oct 2008, 15:15
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