The circumferences of two circle are 132 metres and 176 metres respectively. What is the difference between the area of the larger circle and the smaller circle ?

Solution (By Examveda Team)

$$\eqalign{ & \Rightarrow 2\pi {R_1} = 132 \cr & \Rightarrow {R_1} = \frac{{132 \times 7}}{{2 \times 22}} \cr & \Rightarrow {R_1} = 21\,m \cr & \Rightarrow 2\pi {R_2} = 176 \cr & \Rightarrow {R_2} = \frac{{176 \times 7}}{{2 \times 22}} \cr & \Rightarrow {R_2} = 28\,m \cr & \therefore {\text{Required difference :}} \cr & = \pi \left( {R_2^2 - R_2^2} \right) \cr & = \pi \left( {{R_2} + {R_1}} \right)\left( {{R_2} - {R_1}} \right) \cr & = \left( {\frac{{22}}{7} \times 49 \times 7} \right){m^2} \cr & = 1078\,{m^2} \cr} $$