Cutting square

We cut the circle with the highest possible diameter from a square with a side of 30 cm. How many percent of the square area is this circle?

Final Answer:

p =  78.5398 %

Step-by-step explanation:

$$\begin{gathered} a=30\text{cm} \\ r=a/2=30/2=15\text{cm} \\ {S}_1=a^2=30^2=900{\text{cm}}^2 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 15^2\doteq 706.8583{\text{cm}}^2 \\ p=100\cdot \frac{S_2}{S_1}=100\cdot \frac{706.8583}{900}=78.5398\% \end{gathered}$$

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