Question

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

• A. $32cm$
• B. $35cm$
• C. $23cm$
• D. $48cm$

Answer 1

Answer: (B)

$35cm$

Let the radius of the inner circle be $r$ and the 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, $\pi (R^2-r^2)=808.5$

$\Rightarrow {\left(\frac{77}{2}\right)}^2-r^2=\frac{808.5\times 7}{22}$

$\Rightarrow \frac{5929}{4}-r^2=257.25$

$\Rightarrow r^2=1225$

$\Rightarrow r=35$

Thus, Radius of the inner circle $=35cm$