Question

If the perimeter of a circle is equal to that of a square, then the ratio of area of circle to the square is ______.

• A. 22 : 07
• B. 14 : 11
• C. 7 : 22
• D. 11 : 14

Answer 1

The correct option is B

14 : 11

Let $a$ be the side of the square and $r$ be the radius of the circle.

Given, $4a=2\pi r\Rightarrow a=\frac{\pi r}{2}$

Ratio of the areas of circle to square is
$\pi r^2:a^2$

$\Rightarrow \pi r^2:(\frac{\pi r}{2}{)}^2$

$\Rightarrow 1:\frac{\pi }{4}$

$\Rightarrow 4:\frac{22}{7}$

$\Rightarrow 28:22\Rightarrow 14:11$