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 :

Solution(By Examveda Team)

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

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