# Waste

How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?

Correct result:

p =  36.338 %

#### Solution:

$r=1 \ \text{m} \ \\ u=2r \ \\ \ \\ u=2 \cdot \ r=2 \cdot \ 1=2 \ \text{m} \ \\ a=u/\sqrt{ 2 }=2/\sqrt{ 2 } \doteq \sqrt{ 2 } \ \text{m} \doteq 1.4142 \ \text{m} \ \\ \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 1^2 \doteq 3.1416 \ \text{m}^2 \ \\ S_{2}=a^2=1.4142^2=2 \ \text{m}^2 \ \\ \ \\ p=100 \cdot \ \dfrac{ S_{1}-S_{2} }{ S_{1} }=100 \cdot \ \dfrac{ 3.1416-2 }{ 3.1416 }=36.338 \%$

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