Question

A circle is inscribed in a square. If the area of the square is $36$ sq. units, what is the area of the circle?

• A. $6\pi$
• B. $9\pi$
• C. $12\pi$
• D. $18\pi$
• E. $36\pi$

Answer 1

The correct option is B $9\pi$

Area of square with side $a$ is $a^2$ and area of circle with radius $r$ is $\pi r^2$.

Area of square $=$ $36$ sq units.

Hence, side $=$ $\sqrt{36}=6$ units.

As circle is inscribed in square, so the diameter of the circle $=$ $6$.

If the diameter of the circle is $6$ then the radius of the circle is $3$ as the radius is half of diameter.

Hence, the area of the circle is $\pi (3{)}^2=9\pi$.