JAMB 2002 · UME · Q7

Plane mensuration

In the diagram are two concentric circles of radii $r$ and $R$ with centre $O$ . If $r = \frac25R$ , express the area of the shaded ring in terms of $\pi$ and $R$ .

Worked solution (try it first)

The ring is the big circle minus the small one: $\pi R^2 - \pi r^2$ .
With $r = \frac25R$ , $r^2 = \frac4{25}R^2$ .
So the ring is $\pi R^2 - \frac4{25}\pi R^2 = \frac{21}{25}\pi R^2$ , option C.

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