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Question from Gmat Prep- Help please! 7

Expert replies
by bobdylan » Wed Apr 18, 2012 5:34 am
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 wir is left over. Which of the following represents the total area, in square meters, of the circular and the square region, in terms of r:
a) πr^2
b) π^2 +10
c) πr^2 +1/4 π^2r^2
d) πr^2+(40-2πr)^2
e)πr^2 +(10-1/2 πr)^2
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Source: — Problem Solving |

by aneesh.kg » Wed Apr 18, 2012 5:49 am
The length of the first piece is 2(pi)r and the other is (40 - 2(pi)r).
So side of the square = (40 - 2(pi)r)/4 = (10 - (pi)r/2)

Total area = Area of Circle + Area of Square
= (pi)r^2 + (10 - (pi)r/2)^2

(E) is the answer.
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by Anurag@Gurome » Wed Apr 18, 2012 6:13 am
bobdylan wrote: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 wir is left over. Which of the following represents the total area, in square meters, of the circular and the square region, in terms of r:
a) πr^2
b) π^2 +10
c) πr^2 +1/4 π^2r^2
d) πr^2+(40-2πr)^2
e)πr^2 +(10-1/2 πr)^2
The length of one piece = 2(pi)r and the other is a square. Let us assume that each side of the square is "a".
Perimeter of square = 4a
Now, 2(pi)r + 4a = 40
4a = 40 - 2(pi)r
a = [40 - 2(pi)r]/4 = 10 - (pi)r/2

Total area = Area of Circle + Area of Square
= (pi)r² + a²
= (pi)r² + (10 - (pi)r/2)²

The correct answer is E.
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