Question

In the adjoining figure, the area enclosed between two concentric circles is 770 cm² and the radius of the outer circle is 21 cm. Find the radius of the inner circle.
Figure

Answer 1

Let R and r be the outer and inner radii of a ring.
Then, area of the ring = $\mathrm{\pi }\left({\mathrm{R}}^2-{\mathrm{r}}^2\right)$
Given, R = 21 cm
Area of the ring = 770 cm²
Thus,
$770=\frac{22}{7}\left\{{\left(21\right)}^2-r^2\right\}$
$\Rightarrow \frac{770\times 7}{22}=441-r^2$
⇒ 245 - 441 = - r²
⇒ - 196 = - r²
⇒ 196 = r²
⇒ r = 14 cm
Therefore, inner radius = 14 cm