Question

A Circle is inscribed in a square of side 10 units. What would be the ratio of the circumference of the circle to the perimeter of the square if the sides of the square were changed to S?

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{2}$

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


$d=S$
Circumference of the circle $=\pi d$
Circumference of the circle $=\pi \times S$

Now , $\frac{\text{Circumference of the Circle}}{\text{Perimeter of the square}}=\frac{\pi S}{4\times S}$

$\frac{\text{Circumference of the Circle}}{\text{Perimeter of the square}}=\frac{\pi }{4}$
Hence, the ratio of the circumference of the circle to the perimeter of square if the sides of the square were changed to $S$, remains unchanged equal to $\frac{\pi }{4}$