Circular ring

A square with an area of 16 centimeters is inscribed circle k1 and described to circle k2. Calculate the area of the circular ring, which circles k1, and k2 form.

Correct answer:

S =  12.5664 cm²

Step-by-step explanation:

$$\begin{gathered} S_3=16{\text{cm}}^2 \\ a=\sqrt{S_3}=\sqrt{16}=4\text{cm} \\ {r}_1=a/2=4/2=2\text{cm} \\ {r}_2=\sqrt{2}\cdot r_1=\sqrt{2}\cdot 2=2\sqrt{2}\text{cm}\doteq 2.8284\text{cm} \\ {S}_1=\pi \cdot r_1^2=3.1416\cdot 2^2\doteq 12.5664{\text{cm}}^2 \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 2.8284^2\doteq 25.1327{\text{cm}}^2 \\ S=S_2-S_1=25.1327-12.5664=12.5664{\text{cm}}^2 \end{gathered}$$

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