Waste - cutting metal

In the workshop, they cut 50 circles with a diameter of 9 cm from a rectangular sheet with dimensions of 50 cm and 100 cm. What percentage of the sheet was a waste?

Correct answer:

p =  36.3827 %

Step-by-step explanation:

$$\begin{gathered} a=50\text{cm} \\ b=100\text{cm} \\ D=9\text{cm} \\ r=D/2=9/2=\frac{9}{2}=4.5\text{cm} \\ n=50 \\ {S}_1=a\cdot b=50\cdot 100=5000{\text{cm}}^2 \\ {S}_2=n\cdot \pi \cdot r^2=50\cdot 3.1416\cdot 4.5^2\doteq 3180.8626{\text{cm}}^2 \\ p=100\cdot \frac{S_1-S_2}{S_1}=100\cdot \frac{5000-3180.8626}{5000}=36.3827\% \end{gathered}$$

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