Can you help me work out the length of the wire used to make the paper clip  please?

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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

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.

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kspcr111 | In Training Educator

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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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