Question

In the given figure, the area enclosed between two concentric circles is $808.5c{m}^2$. The circumference of the outer circle is $242cm$. Find the width of the ring.

• A. $1.2cm$
• B. $2.4cm$
• C. $3.5cm$
• D. $4.2cm$

Answer 1

The correct option is C $3.5cm$

Let radius of the inner circle be $r$ and radius of the outer circle be $R$
Area enclosed between the two concentric circles $=\pi (R^2-r^2)$
Given $2\pi R=242$
$\Rightarrow R=\frac{242\times 7}{22\times 2}$
$\Rightarrow R=\frac{77}{2}$
Now, $\pi (R^2-r^2)=808.5$
$\Rightarrow {\left(\frac{77}{2}\right)}^2-r^2=\frac{808.5\times 7}{22}$
$\Rightarrow \frac{5929}{4}-r^2=257.25$
$\Rightarrow r^2=1225$
$\Rightarrow r=35$
Radius of the inner circle $=35cm$
$\therefore$ width of the ring $=(R-r)$
$=(38.5-35)cm$
$=3.5cm$