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

Question:

The areas of two concentric circles are 1386 cm2 and 962.5 cm2. The width of the ring is
(a) 2.8 cm
(b) 3.5 cm
(c) 4.2 cm
(d) 3.8 cm

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 $=(R-r)$

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

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

$=3.5 \mathrm{~cm}$