Question

If the area of region bounded by the inscribed and circumscribed circles of a square is $9\pi$, then the area of the square will be

• A. $6\pi$
• B. $5\pi$
• C. $25$
• D. $36$

Answer 1

The correct option is D $36$

Area of the circumscribed circle of a square is double the area of the circle inscribed in it.

Area of the inscribed circle $=\pi {\left(\frac{a}{2}\right)}^2$ where, $a=$ side of the square
$\therefore 2\pi {\left(\frac{a}{2}\right)}^2-\pi {\left(\frac{a}{2}\right)}^2=9\pi$
On solving we get, $a=6$
$\therefore$ area of the square $=6^2=36$