Question

If radius of circle is decreased by 10% then there is ................ decrease in its area.

• A. 10%
• B. 21%
• C. 19%
• D. 20%

Answer 1

Answer: (C)

19%

Let the radius of original circle = r
$\therefore$ Area of original circle $=\pi r^2$
But, the radius of the circle is decreased by 10%.
$\therefore$ Radius of new circle $R=r-\frac{10r}{100}=\frac{9}{10}r$
Area of new circle $=\pi R^2$
$=\pi \times {\left(\frac{9}{10}r\right)}^2$
$=\frac{81}{100}\pi r^2$
Decrease in area $=\pi r^2-\frac{81}{100}\pi r^2=\frac{19}{100}\pi r^2$
Percentage decrease in area $=\frac{\frac{19}{100}\pi r^2}{\pi r^2}\times 100=19\%$