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