In the diagram are two concentric circles of radii r and R respectively with centre O. If r = 25 2 5 R, express the area of the shaded portion in terms of π...

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

Answer Details

A$\text{shaded portion}$ = $\pi R^2-\pi r^2$ r = $\frac{2}{5}$R

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

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