Question

The area enclosed between two concentric circles is $770c{m^2}$. If the radius of the outer circle is $21cm$, calculate the radius of the inner circle.A. 7cmB. 14cmC. 2.1cmD. 35cm

Let radius of the inner circle be $r$and radius of the outer circle be $R = 21cm$
Area enclosed between the two concentric circles $= \pi \left( {{R^2} - {r^2}} \right) = 770c{m^2}$
$\Rightarrow 770 = \pi \left( {{R^2} - {r^2}} \right) \\ \Rightarrow 770 = \dfrac{{22}}{7}\left( {{{21}^2} - {r^2}} \right) \\ \Rightarrow \dfrac{{770 \times 7}}{{22}} = 441 - {r^2} \\ \Rightarrow 245 = 441 - {r^2} \\ \Rightarrow {r^2} = 196 \\ \Rightarrow r = \sqrt {196} \\ \Rightarrow r = 14 \\$