document.write( "Question 1152181: A piece of wire 10 m long is to be cut into two pieces. One piece is bent into a square, and the other into a circle. How can the wire be cut so that the area enclosed by the two shapes is minimized? Give your answer to the nearest tenth. \n" ); document.write( "

Algebra.Com's Answer #774137 by math_helper(2461) $\"\"$ $\"About$

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document.write( "  0         c                      L\r
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document.write( "Given L=10m, find c such that  a circle made from the material 0..c and a 
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document.write( "square made from the material c..L  have minimum area.\r
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document.write( " A_circle = \r
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document.write( " A_square = \r
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document.write( "A_total (= A) = A_circle + A_square = \r
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document.write( "Take derivative of A wrt c:
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document.write( "dA/dc =  = \r
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document.write( "[ Note that  so the curve is concave up, thus the critical point we are about to find is a local minimum]\r
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document.write( "Set first deriv. to zero & solve for c:  c = 4.39901m  (or  to one decimal place) 
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document.write( "I have separately verified that this value of c minimizes the total area.  You should also verify it to convince yourself.   Also a good idea is to plug in the extreme values of c (0, 10) to gain an understanding of the possible areas.  Here is a graph of A(c) to help you visualize:\r
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