Question 58055: A piece of wire 10m long is cut into two pieces one piece is bent into a square and the other is bent into a circle. Express the total area A of the square and circle as a function of x, th elength of the sides of the square. how should the wire be cut so that the total area enclosed is a minimum? what is the total enclosed area?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A piece of wire 10m long is cut into two pieces one piece is bent into a square and the other is bent into a circle. Express the total area A of the square and circle as a function of x, th elength of the sides of the square. how should the wire be cut so that the total area enclosed is a minimum? what is the total enclosed area?
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One piece is "x" m long; the other is "10-x" m long.
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Using x to make the square,
each side is x/4 m,
and the area is (x/4)^2=x^2/16 m^2
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Using 10-x to make the circle,
circumference = 2(pi)r=10-x
r=(10-x)/2pi
and area is pi[(10-x)/2pi)^2= (4/pi)(10-x)^2
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Total area = (x^2/16)+(4/pi)(10-x)^2
Mimumum at 9.53... using a TI-83 calculator
Area when x=9.53... is 5.9576 m^2
Cheers,
Stan H.
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