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Ï€ is Pi

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Ï€ is Pi

by sanju09 » Fri Mar 18, 2011 2:13 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 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? (Ï€ is Pi)
A. π r^2
B. π r^2 + 10
C. π r^2 + ¼ π^2 r^2
D. π r^2 + (40 - 2 π r)^2
E. π r^2 + (10 - ½ π r)^2



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by 6983manish » Fri Mar 18, 2011 2:30 am
sanju09 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 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? (Ï€ is Pi)
A. π r^2
B. π r^2 + 10
C. π r^2 + ¼ π^2 r^2
D. π r^2 + (40 - 2 π r)^2
E. π r^2 + (10 - ½ π r)^2



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Total length = 40

Circumference of circle = 2Ï€r
Let length of one side of square = x
Perimeter of square = 4x

Hence , 4x + 2Ï€r = 40
x = (40-2Ï€r)/4

Area of both = x^2 + πr^2 = πr^2 + [(40-2πr)/4]^2
= πr^2 + [ 10 - ½πr]^2

Hence answer is E.
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