Question

In a circle of radius 7 cm, a square ABCD is inscribed. Find the area of the circle which is outside the square. [CBSE 2011]

Answer 1

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
$$\begin{gathered} =\mathrm{\pi }{r}^2-\frac{1}{2}{d}^2 \\ =\frac{22}{7}\times {\left(7\right)}^2-\frac{1}{2}\times {\left(14\right)}^2 \\ =56{\mathrm{cm}}^2 \end{gathered}$$

Hence, the required area is 56 cm² .