In the diagram are two concentric circles of ra... - JAMB Mathematics 2002 Question

In the diagram are two concentric circles of radii r and R respectively with centre O. If r = \(\frac{2}{5}\)R, express the area of the shaded portion in terms of \(\pi\) and R

\(\frac{5}{9} \pi R^2\)

\(\frac{21}{25} \pi R^2\)

\(\frac{21}{23} \pi R^2\)

\(\frac{9}{25} \pi R^2\)

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Correct Option: B

A_{(\text{shaded portion})} = (\pi R^2 - \pi r^2) r = (\frac{2}{5})R

A_{(\text{shaded portion})} = (\pi R^2 - \pi (\frac{2}{3} R)^2 = \pi R^2 - \frac{4 \pi R^2}{25})

= (\pi R^2(1 - \frac{2}{3}) = \frac{21}{25} \pi R^2)

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