Concentric circles

There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?

Correct result:

r₂ =  5.6569 cm

Solution:

$$\begin{gathered} r=8\text{ cm } \\ S=\pi \cdot r^2=3.1416\cdot 8^2\doteq 201.0619{\text{cm}}^2 \\ {S}_2=S\mathrm{/}2=201.0619\mathrm{/}2\doteq 100.531{\text{cm}}^2 \\ {S}_2=\pi \cdot r_2^2 \\ {r}_2=\sqrt{S_2\mathrm{/}\pi }=\sqrt{100.531\mathrm{/}3.1416}=4\sqrt{2}=5.6569\text{ cm} \end{gathered}$$

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