# Circles

The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.

Correct result:

r =  3.2

#### Solution:

$\dfrac{S_1}{S_2} = \dfrac{\pi r^2}{\pi \dfrac{ 20}{ 2}} = \dfrac{ 2}{ 20} \ \\ r = \sqrt{ \dfrac{ 2 }{ 20}} \cdot \dfrac{ 20}{ 2} \doteq 3.2$

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