question_answer

A circular area having a radius 20 cm is divided into two equal parts by a concentric circle of radius 'r? The value of \['r'\] will be

A)  5 cm                       

B)         10 cm

C)  \[5\sqrt{2}\,cm\]           

D)         \[10\sqrt{2}\,cm\]  

Correct Answer: D

Solution :

 Area of circle \[{{C}_{2}}=\frac{1}{2}\] Area of circle \[{{C}_{1}}\] \[\therefore \]  \[\pi \,{{r}^{2}}=\frac{1}{2}\times \pi \times {{20}^{2}}\] or            \[{{r}^{2}}=200\] or            \[r=10\sqrt{2}\]