Question

Let $C$ and $A$ be the circumference and the area of a circle respectively. If $xC$ is the circumference of another circle whose area is $2A$, then $x$ equals

• A. $2\sqrt{2}$
• B. $2$
• C. $\sqrt{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $\sqrt{2}$

Since, $C=\pi r$ & $A=\pi r^2$

By given, circumference & area of new circle, $C_1=xC$

& $A_1=2A$

$\Rightarrow \pi (r_1{)}^2=2(\pi r^2)$

$\Rightarrow r_1=\sqrt{2}r$
Now, equating the circumferences,
$C_1=xC\Rightarrow 2\pi r_1=x\left(2\pi r\right)$
$\Rightarrow \sqrt{2}r=x\times r$
$\Rightarrow x=\sqrt{2}$