Question

The area enclosed between the concentric circles is 770 cm². If the radius of the outer circle is 21 cm, find the radius of the inner circle.

Answer 1

Let the radius of outer and inner two circles be r₁ and r₂ respectively.
Area enclosed between concentric circles = $\mathrm{\pi }{r_1}^2-\mathrm{\pi }{r_2}^2$
$$\begin{gathered} \Rightarrow 770=\frac{22}{7}\left({21}^2-{r_2}^2\right) \\ \Rightarrow 245={21}^2-{r_2}^2 \\ \Rightarrow {r_2}^2=441-245 \\ \Rightarrow {r_2}^2=196 \\ \Rightarrow {r_2}^2={14}^2 \\ \Rightarrow r_2=14\mathrm{cm} \end{gathered}$$

Hence, the radius of inner circle is 14 cm.