# The area enclosed between the concentric circles is

Question:

The area enclosed between the concentric circles is $770 \mathrm{~cm}^{2}$. If the radius of the outer circle is $21 \mathrm{~cm}$, find the radius of the inner circle.

Solution:

Let the radius of outer and inner two circles be r1  and r2 respectively.

Area enclosed between concentric circles $=\pi r_{1}{ }^{2}-\pi r_{2}{ }^{2}$

$\Rightarrow 770=\frac{22}{7}\left(21^{2}-r_{2}^{2}\right)$

$\Rightarrow 245=21^{2}-r_{2}^{2}$

$\Rightarrow r_{2}^{2}=441-245$

$\Rightarrow r_{2}^{2}=196$

$\Rightarrow r_{2}^{2}=14^{2}$

$\Rightarrow r_{2}=14 \mathrm{~cm}$

Hence, the radius of inner circle is 14 cm.