Question

A square is inscribed in a circle. The area of the square is what percent of the area of the circle?

• A. $63.7\%$
• B. $45.4\%$
• C. $75.8\%$
• D. $85.6\%$

Answer 1

The correct option is A $63.7\%$

Let the radius of the circle be $r$.

Therefore, Diameter of the circle = Diagonal of the square $=2r$

Let the length of side of square be $x$.

By Pythagoras theorem,

$(2r{)}^2=x^2+x^2$

$4r^2=2x^2$

Hence, $x=r\sqrt{2}$

Area of the square is $(r\sqrt{2}{)}^2=2r^2$

And the area of the circle is $\pi r^2$

The percentage that the square takes up in circle $=$ $\frac{2r^2}{\pi r^2}\times 100$

$=\frac{2}{\pi }\times 100=\frac{200}{3.14}=63.69$ which is approximately $63.7\%$.