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A 40 meter long wire is cut into 2 pieces. one piece is used

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A 40 meter long wire is cut into 2 pieces. one piece is used [#permalink] New post 12 Mar 2006, 09:33
A 40 meter long wire is cut into 2 pieces. one piece is used to make a circle with radius r, and the other is used to form a square. No wire is left over. Which of the follwing represents the total area in sqaure meters of the circular and the square regions in tems of r.

1.) pi*r^2
2.) pi*r^2 + 10
3.) pi*r^2 + (0.25*pi^2*r^2)
4.) pi*r^2 +(40-(2*pi*r))^2
5.) pi*r^2 + (10-(0.5*pi*r)^2
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 [#permalink] New post 12 Mar 2006, 10:03
It's "E".

Let 'x' be the length of rope used for circle. i.e. circumference x = 2*pi*r
Then rope length used for square is (40-x)

1) Area of circle = pi*(r^2)
2) Area of square:
Length of a side of square = (40-x)/4
Hence, area of square = ((40-x)/4)^2
=> (10 - (x/4))^2
=> (10 - (2*pi*r/4))^2 ------------------------ substitue x = 2*pi*r
=> (10 - (0.5*pi*r))^2

Add 1 & 2, you get "E"
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 [#permalink] New post 12 Mar 2006, 12:07
vivek123 wrote:
It's "E".

Let 'x' be the length of rope used for circle. i.e. circumference x = 2*pi*r
Then rope length used for square is (40-x)

1) Area of circle = pi*(r^2)
2) Area of square:
Length of a side of square = (40-x)/4
Hence, area of square = ((40-x)/4)^2
=> (10 - (x/4))^2
=> (10 - (2*pi*r/4))^2 ------------------------ substitue x = 2*pi*r
=> (10 - (0.5*pi*r))^2

Add 1 & 2, you get "E"


I think this is a real GMAT question, well done vivek, as usual
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 [#permalink] New post 12 Mar 2006, 12:11
conocieur wrote:
vivek123 wrote:
It's "E".

Let 'x' be the length of rope used for circle. i.e. circumference x = 2*pi*r
Then rope length used for square is (40-x)

1) Area of circle = pi*(r^2)
2) Area of square:
Length of a side of square = (40-x)/4
Hence, area of square = ((40-x)/4)^2
=> (10 - (x/4))^2
=> (10 - (2*pi*r/4))^2 ------------------------ substitue x = 2*pi*r
=> (10 - (0.5*pi*r))^2

Add 1 & 2, you get "E"


I think this is a real GMAT question, well done vivek, as usual


Hey conocieur, thanks for encouraging :)
I've been following your posts & you rock! Your mathematics skills are very good! :good
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 [#permalink] New post 12 Mar 2006, 18:22
area of circle = pi * (r^2)
circumference of circle = 2*pi*r

Length of wire left to make square = 40 - 2*pi*r
Area of sqaure = [ (40 - 2*pi*r)/4 ]^2

Total area = (10 - (pi*r)/2)^2 + 2*pi*r

Ans: E
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 [#permalink] New post 12 Mar 2006, 22:44
At what level of difficulty would you guys rate this question?
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 [#permalink] New post 12 Mar 2006, 22:47
I would say this one comes in as a 'easy' type of question. The variable are just there to confuse. All it tests is your ability to recall how to calculate the areas of a square and a cirle and also the perimeter of a circle.
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 [#permalink] New post 13 Mar 2006, 10:50
The two pieces represent the circumference of the circle ( 2*pi*r) and the perimeter of the sqare ( 40 - 2*pi*r ).

Area = pi*r^2 + ( 40 - 2*pi*r )/4*( 40 - 2*pi*r )/4....ANS is E.
  [#permalink] 13 Mar 2006, 10:50
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A 40 meter long wire is cut into 2 pieces. one piece is used

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