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 the radius of the circle $=r.$

$\therefore$ Its circumference $=2\pi r$ and Area $=\pi r^2.$

It is given that circumference of circle is same as perimeter of square.

$\therefore$ Square's one side $=\frac{1}{4}\times$ cirumference of the given circle

$=\frac{1}{4}\times 2\pi r=\frac{\pi r}{2}.$

$\therefore$ Area of square $={\left(\frac{\pi r}{2}\right)}^2.$

So, Area of circle $:$ Area of Square

$=\pi r^2:{\left(\frac{\pi r}{2}\right)}^2=\frac{4}{\pi }=\frac{4}{\frac{22}{7}}=\frac{14}{11}$