Question

A circle is inscribed in a square of side length $6$. The area of the region inside the square but outside the circle is

• A. $36\pi$
• B. $26\pi -9$
• C. $26\pi -36$
• D. $36-9\pi$
• E. $9\pi -36$

Answer 1

Answer: (D)

$36-9\pi$

Each side of the square $=6$

$\therefore$ area of the circle $=$ $6^2=36$

The radius of the inscribed circle $=3$

$\therefore$ area of the circle $=$ $\pi r^2=\pi 3^2=9\pi$

$\therefore$ area of the region inside the square but outside the circle$=36-9\pi$