# Circular ring

Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form.

Result

S =  12.566 cm2

#### Solution:

$S_{3}=16 \ \text{cm}^2 \ \\ a=\sqrt{ S_{3} }=\sqrt{ 16 }=4 \ \text{cm} \ \\ r_{1}=a/2=4/2=2 \ \text{cm} \ \\ r_{2}=\sqrt{ 2 } \cdot \ r_{1}=\sqrt{ 2 } \cdot \ 2 \doteq 2 \ \sqrt{ 2 } \ \text{cm} \doteq 2.8284 \ \text{cm} \ \\ S_{1}=\pi \cdot \ r_{1}^2=3.1416 \cdot \ 2^2 \doteq 12.5664 \ \text{cm}^2 \ \\ S_{2}=\pi \cdot \ r_{2}^2=3.1416 \cdot \ 2.8284^2 \doteq 25.1327 \ \text{cm}^2 \ \\ S=S_{2}-S_{1}=25.1327-12.5664 \doteq 12.5664 \doteq 12.566 \ \text{cm}^2$

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