• anonymous
A piece of wire 4 m long is cut into two pieces. One piece is bent into the shape of a circle of radius r and the other is bent into a square of side s. How should the wire be cut so that the total area enclosed is: a) a maximum? r= and s= . b) a minimum? r= and s=
  • Stacey Warren - Expert
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  • katieb
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  • IrishBoy123
you have 2 equations to play with: \(2 \pi r + 4s = 4\) \(A = \pi r^2 + s^2\) and you want to max/min A you can use lagrange multipliers or use the first equation to make this a single variable calculus problem for A which you solve setting A' = 0. determining the nature of the stationary point might be a bit trickier using the neater lgrannge but the you might also know that the circle gives you the largest area for a given perimeter/ circumference, which is why, for example, polar bears are the shape they are.

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