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

A
\(\frac{5}{9} \pi R^2\)
B
\(\frac{21}{25} \pi R^2\)
C
\(\frac{21}{23} \pi R^2\)
D
\(\frac{9}{25} \pi R^2\)
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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