Homework Soursea 10 cm wire is cut into two pieces one piece is bent into a
a 10 cm wire is cut into two pieces. one piece is bent into a square and another is bent into a circle. how should the wire be cut so that the total area is maximal ? How should the wire be cut so that the area is minimal ?
Solution
x=2*pi*r 10-x=4*l 10-2*pi*r=4*l Area=pi*r^2+l^2=pi*r^2+((10-2*pi*r)/4)^2 Derivative=1/2*pi*((4+pi)*r-5)=0 r=5/(4+pi)=.70 x=1.4*pi=4.40 Area=3.5 is the minimum when circle piece is 4.4 cm and square piece is 5.6 cm For max: make it all circle r=10/(2*pi)=1.59 Area=pi*1.59^2=7.94
