Cutting circles

From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste?

Correct result:

n =  25
p =  21.4602 %

Solution:

r=10 cm a=1⋅ 100=100 cm S1=a2=1002=10000 cm2 D=2⋅ r=2⋅ 10=20 cm S2=D2=202=400 cm2 n=S1/S2=10000/400=25
S3=π⋅ r2=3.1416⋅ 102≐314.1593 cm2 p=100⋅ (S1−n⋅ S3)/S1=100⋅ (10000−25⋅ 314.1593)/10000=21.4602%

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