Question

If the perimeter of a circle is equal to that of 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 radius of circle be r and side of square be a.

According to the given condition,

Perimeter of a circle = Perimeter of a square

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

Now,

$\frac{Areaofcircle}{Areaofsquare}$

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

$=\frac{\pi r^2}{\frac{{\pi }^2{r}^2}{4}}=\frac{4}{\pi }=\frac{4}{\frac{22}{7}}$

$=\frac{28}{22}=\frac{14}{11}$