Question

A Circle is inscribed in a Square. The side length of the square is 10 cm. The ratio of the circumference of circle to the Perimeter of square is

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

Answer 1

Answer: (A), (C)

$\frac{\pi }{4}$

A Circle is inscribed in a Square.



The side length of the square is 10.
As the circle is inscribed in the square.

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



$d=10$
Circumference of the circle
$=\pi d$
$=\pi \times 10$

Now , $\frac{\text{Circumference of the Circle}}{\text{Perimeter of the square}}$
$=\frac{10\pi }{4\times Side}$

$\frac{\text{Circumference of the Circle}}{\text{Perimeter of the square}}$
$=\frac{10\pi }{4\times 10}$

$\frac{\text{Circumference of the Circle}}{\text{Perimeter of the square}}$
$=\frac{10\pi }{40}$
$=\frac{\pi }{4}$