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The area enclosed between the concentric circles is $770\ cm^2$. If the radius of the outer circle is $21\ cm$, find the radius of the inner circle.
Given:
The area enclosed between the concentric circles is $770\ cm^2$.
The radius of the outer circle is $21\ cm$.
To do:
We have to find the radius of the inner circle.
Solution:
Let $r$ be the radius of the inner circle.
Area of a circle of radius $r=\pi r^2$
According to the question,
$\pi (21)^{2}-\pi r^{2}=770$
$\frac{22}{7}(21)^{2}-\frac{22}{7} r^{2}=770$
$\frac{22}{7} \times 441-\frac{22}{7} r^{2}=770$
$\Rightarrow 1386-\frac{22}{7} r^{2}=770$
$\Rightarrow \frac{22}{7} r^{2}=1386-770$
$\Rightarrow \frac{22}{7} r^{2}=616$
$\Rightarrow r^{2}=\frac{616 \times 7}{22}$
$\Rightarrow r^{2}=28 \times 7$
$\Rightarrow r^{2}=196$
$\Rightarrow r^{2}=(14)^{2}$
$\Rightarrow r=14\ cm$
The radius of the inner circle is $14\ cm$.