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1. 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 ?

A. 1048 m²

B. 1076 m²

C. 1078 m²

D. 1090 m²

Solution:

\begin{aligned} \Rightarrow 2 π R_{1} = 132 \\ \Rightarrow R_{1} = \frac{132 \times 7}{2 \times 22} \\ \Rightarrow R_{1} = 21 m \\ \Rightarrow 2 π R_{2} = 176 \\ \Rightarrow R_{2} = \frac{176 \times 7}{2 \times 22} \\ \Rightarrow R_{2} = 28 m \\ ∴ Required difference : \\ = π (R_{2}^{2} - R_{2}^{2}) \\ = π (R_{2} + R_{1}) (R_{2} - R_{1}) \\ = (\frac{22}{7} \times 49 \times 7) m^{2} \\ = 1078 m^{2} \end{aligned}

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