Square metal sheet

Four squares of 300 mm side were cut out from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.

Correct result:

f =  0.265
p =  26.5 %

Solution:

$a=0.7 \ \text{m} \ \\ b=300 \ mm \rightarrow m=300 / 1000 \ m=0.3 \ m \ \\ \ \\ S_{1}=a^2=0.7^2=\dfrac{ 49 }{ 100 }=0.49 \ \text{m}^2 \ \\ S_{2}=4 \cdot \ b^2=4 \cdot \ 0.3^2=\dfrac{ 9 }{ 25 }=0.36 \ \\ \ \\ o=S_{1}-S_{2}=0.49-0.36=\dfrac{ 13 }{ 100 }=0.13 \ \text{m}^2 \ \\ f=\dfrac{ o }{ S_{1} }=\dfrac{ 0.13 }{ 0.49 }=\dfrac{ 13 }{ 49 }=0.265$
$p=100 \cdot \ f=100 \cdot \ 0.2653=\dfrac{ 53 }{ 2 }=26.5 \%$

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