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

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### 2 Answers

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 .