Question

Given a Circle is inscribed in a square of side each 10 cm. What is the ratio of the area of the circle to the area of the square?

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{8}$

Answer 1

The correct option is 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.


$d=10$
$\therefore r=\frac{d}{2}$
$r=5$


Area of the circle $=\pi r^2$
Area of the circle $=\pi \times (5{)}^2$
$=\pi \times 25$
Now , $\frac{\text{Area of the Circle}}{\text{Area of the square}}=\frac{\pi r^2}{\text{Side}\times \text{Side}}$

$\frac{\text{Area of the Circle}}{\text{Area of the square}}=\frac{\pi (5{)}^2}{10\times 10}$



$\frac{\text{Area of the Circle}}{\text{Area of the square}}=\frac{\pi \cdot 25}{100}=\frac{\pi }{4}$