Question

In the figure shown, if the area of the shaded region is $3$ times the area of the smaller circular region, then the ratio of the circumference of the larger circle to the circumference of the smaller circle is equal to

• A. $4$
• B. $3$
• C. $2$
• D. $\sqrt{3}$
• E. $\sqrt{2}$

Answer 1

The correct option is C $2$

Let the radius of the larger circle be $R$ and the radius of the smaller circle be $r$.

$\therefore$ Area of shaded region $=$ $\pi (R^2-r^2)$

But it is given that the area of the shaded region is equal to 3 times the area of the smaller circle. So,

$\pi (R^2-r^2)=3\pi r^2$

$\Rightarrow R^2={4r}^2$

$\Rightarrow R=2r$

Now, ratio of circumference of larger circle to that of smaller circle will be,

$\frac{2\pi R}{2\pi r}=\frac{R}{r}$

$=\frac{2r}{r}$

$=2:1$

Hence, option $C$ is correct.