The areas of two concentric circles are 1386 cm2 and 962.5 cm2.

Solution:

 (b) 3.5 cm
Let r cm and R cm be the radii of two concentric circles.
Thus, we have:

$\pi \mathrm{R}^{2}=1386$

$\Rightarrow \frac{22}{7} \times R^{2}=1386$

$\Rightarrow R^{2}=\left(1386 \times \frac{7}{22}\right) \mathrm{cm}^{2}$

$\Rightarrow R^{2}=441 \mathrm{~cm}^{2}$

 

$\Rightarrow R=21 \mathrm{~cm}$

Also,

$\pi \mathrm{r}^{2}=962.2$

$\Rightarrow \frac{22}{7} \times \mathrm{r}^{2}=962.2$

$\Rightarrow \mathrm{r}^{2}=\left(962.2 \times \frac{7}{22}\right) \mathrm{cm}^{2}$

$\Rightarrow \mathrm{r}^{2}=\left(\frac{962.2}{10} \times \frac{7}{22}\right) \mathrm{cm}^{2}$

$\Rightarrow \mathrm{r}^{2}=\frac{1225}{4} \mathrm{~cm}^{2}$

 

$\Rightarrow r=\frac{35}{2} \mathrm{~cm}$

$\therefore$ Width of the ring $=(R-r)$

$=\left(21-\frac{35}{2}\right) \mathrm{cm}$

$=\frac{7}{2} \mathrm{~cm}$

 

$=3.5 \mathrm{~cm}$