Question

If radius of the circle is decreased by $10\%$, then there is _______ decrease in its area.

• A. $10\%$
• B. $21\%$
• C. $19\%$
• D. $20\%$

Answer 1

The correct option is C $19\%$

Let the radius of the circle be $r$.
$\therefore$ Its area $A_1=\pi r^2$
Now, radius of the circle is decreased by $10\%$
$\therefore$ New radius $R=r-\frac{10}{100}r=\frac{9r}{10}$
$\therefore$ New area $A_2=\pi R^2$
$=\pi {\left(\frac{9r}{10}\right)}^2=\frac{81}{100}\pi r^2$
$\therefore$ Decrease in its area
$=A_1-A_2$
$=\pi r^2-\frac{81}{100}\pi r^2$
$=\frac{19}{100}\pi r^2$
Decrease in its area in $\%=19\%$