Question

The area of the concentric circles are $962.5c{m}^2$ and $1368c{m}^2$. Find the width of the ring formed by them.

• A. $2.1cm$
• B. $1cm$
• C. $5.5cm$
• D. $3.5cm$

Answer 1

Answer: (D)

$3.5cm$

Let the radii of the bigger and smaller circles be $Rcm$ and $rcm$, respectively.

Now, Area of the bigger circle $=\pi R^2$

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

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

$\Rightarrow R^2=441$

$\Rightarrow R=21$

$\therefore$ Radius of bigger circle $\left(R\right)=21cm$

Similarly, Area of the smaller circle $=\pi r^2$

$\Rightarrow 962.5=\frac{22}{7}\times r^2$

$\Rightarrow r^2=\frac{962.5\times 7}{22}$

$\Rightarrow r^2=306.25$

$\Rightarrow r=17.5$

$\therefore$ Radius of smaller circle $\left(r\right)=17.5cm$

Hence, Width of Ring $=R-r=21-17.5=3.5cm$

Thus, $\text{D}$ is the correct option.