Question:
In a circle of radius 7 cm, a square ABCD is inscribed. Find the area of the circle which is outside the square.
Solution:
Let the diagonal of the square be d.
We know that if a circle circumscribes a square, then the diameter of the circle is equal to the diagonal of the square.
∴ d = 2 ⨯ 7 = 14 cm
Now,
Area of required region = Area of circle − Area of square
$=\pi r^{2}-\frac{1}{2} d^{2}$
$=\frac{22}{7} \times(7)^{2}-\frac{1}{2} \times(14)^{2}$
$=56 \mathrm{~cm}^{2}$
Hence, the required area is 56 cm2 .