If the radius of a circle is diminished by 10%, then its area is diminished by
(a) 10%
(b) 19%
(c) 20%
(d) 36%
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).
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