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?

Result

r2 =  5.657 cm

Solution:

r=8 cm  S=π⋅ r2=3.1416⋅ 82≐201.0619 cm2  S2=S/2=201.0619/2≐100.531 cm2  S2=π⋅ r22  r2=S2/π=100.531/3.1416≐4 2≐5.6569≐5.657 cmr=8 \ \text{cm} \ \\ \ \\ S=\pi \cdot \ r^2=3.1416 \cdot \ 8^2 \doteq 201.0619 \ \text{cm}^2 \ \\ \ \\ S_{2}=S/2=201.0619/2 \doteq 100.531 \ \text{cm}^2 \ \\ \ \\ S_{2}=\pi \cdot \ r_{2}^2 \ \\ \ \\ r_{2}=\sqrt{ S_{2}/\pi }=\sqrt{ 100.531/3.1416 } \doteq 4 \ \sqrt{ 2 } \doteq 5.6569 \doteq 5.657 \ \text{cm}

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