Cutting circles

From a square sheet with 1 m sides, we cut out circles with a radius of 10 cm. How many discs can we cut, and what percentage of the material will be wasted?

Final Answer:

n =  25
p =  21.4602 %

Step-by-step explanation:

$$\begin{gathered} r=10\text{cm} \\ a=1\cdot 100=100\text{cm} \\ {S}_1=a^2=100^2=10000{\text{cm}}^2 \\ D=2\cdot r=2\cdot 10=20\text{cm} \\ {S}_2=D^2=20^2=400{\text{cm}}^2 \\ n=S_1/S_2=10000/400=25 \end{gathered}$$

$$\begin{gathered} S_3=\pi \cdot r^2=3.1416\cdot 10^2\doteq 314.1593{\text{cm}}^2 \\ p=100\cdot (S_1-n\cdot S_3)/S_1=100\cdot (10000-25\cdot 314.1593)/10000=21.4602\% \end{gathered}$$

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