Quarter of a circle

Calculate the circumference of a quarter circle if its content is S = 314 cm².

Correct answer:

o =  71.3978 cm

Step-by-step explanation:

$$\begin{gathered} S=314{\text{cm}}^2 \\ S={\displaystyle \frac{\pi \cdot r^2}{4}} \\ r=\sqrt{4\cdot S\mathrm{/}\pi }=\sqrt{4\cdot 314\mathrm{/}3.1416}\doteq 19.9949\text{ cm } \\ o=2\cdot r+2\pi \cdot r\mathrm{/}4=2\cdot 19.9949+2\cdot 3.1416\cdot 19.9949\mathrm{/}4=71.3978\text{ cm} \end{gathered}$$

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