Metal washers

Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet.

Correct result:

p =  35.1075 %
p2 =  49.7345 %

Solution:

a=10 cm D=80 mm cm=80/10  cm=8 cm  r=D/2=8/2=4 cm  S1=π r2=3.1416 4250.2655 cm2  (2r)2=b2+(a2 r)2  b=(2r)2(a2 r)2=(2 4)2(102 4)2=2 15 cm7.746 cm  S2=a b=10 7.746=20 15 cm277.4597 cm2  p=S2S1S2 100=77.459750.265577.4597 100=35.1075%
S3=a2=102=100 cm2  p2=100 S3S1S3=100 10050.2655100=49.7345%



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