Question

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ____.

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

Answer 1

The correct option is B 14 : 11

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

According to the question,
Perimter of the circle = Perimeter of the square

$\Rightarrow 2\pi r=4a$
$\Rightarrow a=\frac{\pi r}{2}$
Area of the circle = $\pi r^2$
Area of the square = $a^2$

Now, ratio of their areas
$=\frac{\text{Area of the circle}}{\text{Area of the square}}$
$=\frac{\pi r^2}{a^2}$

$=\frac{\pi r^2}{(\frac{\pi r}{2}{)}^2}$

$=\frac{\pi r^2}{\frac{{\pi }^2{r}^2}{4}}$

$=\frac{4}{\pi }$

$=\frac{4}{\frac{22}{7}}$

$=\frac{28}{22}$

$=\frac{14}{11}$
$\therefore \text{Option b is correct.}$