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 answer:

p =  36.338 %

Step-by-step explanation:

$$\begin{gathered} r=1\text{ m } \\ u=2r \\ u=2\cdot r=2\cdot 1=2\text{ m } \\ a=u\mathrm{/}\sqrt{2}=2\mathrm{/}\sqrt{2}=\sqrt{2}\text{ m}\doteq 1.4142\text{ m } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 1^2\doteq 3.1416{\text{m}}^2 \\ {S}_2=a^2=1.4142^2=2{\text{m}}^2 \\ p=100\cdot {\displaystyle \frac{S_1-S_2}{S_1}}=100\cdot {\displaystyle \frac{3.1416-2}{3.1416}}=36.338\mathrm{\%} \end{gathered}$$

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