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A thin piece of wire 40 meters long is cut into two pieces. [#permalink]
22 Sep 2005, 20:09
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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. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?
B. Pi*(r)^2 + 10
C. Pi*(r)^2 + 1/4*(Pi)^2*(r)^2
D. Pi*(r)^2 + (40-2*Pi*r)^2
E. Pi*(r)^2 + (10-1/2*Pi*r)^2
E here. since the wire = 40 when cust into 2 pieces one piece is circle with A=pr^2 . the square is a bit tricky since we have to take 1/4th of the remaining part of the wire after we have used the other for the radius of the Circle. 1/4th of the remainder is the side of the square - the side is equal to 10 - 1/2*P*r and the area is [10 - 1/2*P*r] ^2 therefore answer E.