Question

If the radius of a circle is diminished by $10\%$, then its area is diminished by:

• A. $10\%$
• B. $19\%$
• C. $20\%$
• D. $36\%$

Answer 1

The correct option is B $19\%$

Let the radius of the circle be $r$

Then area of cirlce $=\pi r^2$

Given that radius of the circle is diminished by $10\%$

Hence the new radius $=r-\left(10\%ofr\right)=90\%ofr=\frac{9r}{10}$

Area of the new circle $=\pi {\left(\frac{9r}{10}\right)}^2=\frac{81}{100}\pi r^2$

Change in area $\pi r^2-\frac{81}{100}\pi r^2=\frac{19}{100}\pi r^2=0.19\pi r^2$

Percentage of area diminished is $19\%$