Question

A Circle is inscribed in a square. What would be the ratio of area of the circle to the area of square if the sides of square were changed to $S$ ?

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$

Answer 1

The correct option is B $\frac{\pi }{4}$

Given a circle is inscribed in a Square.


If the length of the square is $S$
As the circle is inscribed in the square.


Therefore the diameter of circle is exactly equal to the side of the square $S$.


$d=S$



$r=\frac{S}{2}$
Area of the circle $=\pi r^2$
Area of the circle $=\pi \times {\left(\frac{S}{2}\right)}^2$
$=\pi \times \left(\frac{S^2}{4}\right)$

Now , $\frac{\text{Area of the Circle}}{\text{Area of the square}}$
$=\frac{\pi \times \left(\frac{S^2}{4}\right)}{S\times S}$

$\frac{\text{Area of the Circle}}{\text{Area of the square}}$
$=\frac{\pi }{4}$

Hence, the ratio of the area of the circle to the area of the square if the sides of the square were changed to $S$, remains unchanged equal to $\frac{\pi }{4}$