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# Thin wire question - GMATPrep

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Manager
Joined: 25 May 2009
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Concentration: Finance
GMAT Date: 12-16-2011
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Thin wire question - GMATPrep [#permalink]  31 May 2009, 14:34
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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 the square regions in terms of r?
A) $$xr^2$$
B) $$xr^2 + 10$$
C) $$(pie)r^2 + /frac{1}{4}(pie)^2r^2$$
D) $$(pie)r^2 + (40-2(pie)r)^2$$
E) $$(pie)r^2 + (10 - frac{1}{2} (pie)r)^2$$

[Reveal] Spoiler:
OG=E
Manager
Joined: 08 Feb 2009
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Re: Thin wire question - GMATPrep [#permalink]  31 May 2009, 18:09
Length of the circular piece = 2$$\pi$$r
Other piece = 40 - 2$$\pi$$r

Side of Square = $$\frac{(40 - 2\pi r)}{4}$$ $$\Rightarrow$$ Area = $$(10 - \frac{1}{2} \pi r)^2$$

Length of the circular piece = Circumference of Circle = 2$$\pi$$r $$\Rightarrow$$ Area = $$\pi r^2$$

Manager
Joined: 12 Apr 2006
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Location: India
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Re: Thin wire question - GMATPrep [#permalink]  01 Jun 2009, 01:39
goldeneagle94 wrote:
Length of the circular piece = 2$$\pi$$r
Other piece = 40 - 2$$\pi$$r

Side of Square = $$\frac{(40 - 2\pi r)}{4}$$ $$\Rightarrow$$ Area = $$(10 - \frac{1}{2} \pi r)^2$$

Length of the circular piece = Circumference of Circle = 2$$\pi$$r $$\Rightarrow$$ Area = $$\pi r^2$$

Agree with E.

Re: Thin wire question - GMATPrep   [#permalink] 01 Jun 2009, 01:39
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