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The length of the wire can be calculated by dividing the paper clip into sections of straight length and semicircles (circumference = pi *radius). It would be easier to start with the outer end of the clip.
Length of paper clip = (5-0.9) + pi*(0.9) + (6.8-0.9) + pi*(7.5-6.8) + (6.8-2.1) + pi*(2.1-1.5) + (5-2.1)
= 4.1 + 3.14*0.9 + 5.9 + 3.14* 0.7 + 4.7 + 3.14*0.6 + 2.9 = 24.51 cm.
A,B,C,D,E,F,G,H,I,J,K are the points of intersections of the dotted lines and the wire.....
Now the total length of the wire (L wire) can be calculated as follows,
L wire = length of straight line AB + circumference of semicircle BCD + length of straight line DE + circumference of semicircle EFG + length of straight line GH + circumference of semicircle HIJ + length of straight line JK
= (4.1 cm) + (pi* 0.9) + (5.9 cm) + (pi * 0.7) + (4.7 cm)+ (pi * 0.6)+ (2.9cm)
= (4.1 cm) + (3.14* 0.9) + (5.9 cm) + (3.14 * 0.7) + (4.7 cm)+ (3.14 * 0.6)+ (2.9cm)
= 24.508 cm
[ as the circumference of a semicircle is (Pi* radius) and the value of pi is taken as 3.14 ]
Thus the total length of the wire is 24.508 cm .
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