If the radius of a circle is diminished by 10%,

Let x be the initial radius of the circle.

Therefore, its area is $\pi x^{2}$ .(1)

It is given that the radius is diminished by 10%, therefore, its new radius is calculated as shown below,

new radius $=x-0.10 x$

$\therefore$ new radius $=0.90 x$

$\therefore$ new area $=(0.90 x)^{2}$

$\therefore$ new area $=0.81 x^{2}$

Now we will find the percentage decreased in the area.

$\therefore$ change $=0.81 x^{2}-x^{2}$

$\therefore$ change $=0.19 x^{2}$

Therefore, its area is diminished by $19 \%$.

Hence, the correct answer is option (b).