# 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 =  5.657 cm

#### Solution:

$r=8 \ \text{cm} \ \\ \ \\ S=\pi \cdot \ r^2=3.1416 \cdot \ 8^2 \doteq 201.0619 \ \text{cm}^2 \ \\ \ \\ S_{2}=S/2=201.0619/2 \doteq 100.531 \ \text{cm}^2 \ \\ \ \\ S_{2}=\pi \cdot \ r_{2}^2 \ \\ \ \\ r_{2}=\sqrt{ S_{2}/\pi }=\sqrt{ 100.531/3.1416 }=4 \ \sqrt{ 2 }=5.657 \ \text{cm}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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