The sides of a rectangle are 8 cm and 6 cm. The corners of the rectangle lie on a circle. Find the are a of the circle without the rectangle :

Answer: Option A

Diameter of the circle :
$$\begin{array}{rl}& =AC=\sqrt{{\left(AB\right)}^2+{\left(BC\right)}^2}\\ & =\sqrt{8^2+6^2}\\ & =\sqrt{100}cm\\ & =10cm\end{array}$$
Radius = 5 cm
Required area = (Area of the circle) - (Area of the rectangle)

$$\begin{array}{rl}& =\left[\left(\frac{22}{7}\times 5\times 5\right)-\left(8\times 6\right)\right]c{m}^2\\ & =\left(\frac{550}{7}-48\right)c{m}^2\\ & =\left(\frac{214}{7}\right)c{m}^2\\ & =30.57c{m}^2\approx 30.6c{m}^2\end{array}$$