Question : The radius of a circle is increased by 10%. The percentage increase in its area is:
Option 1: 10%
Option 2: 11%
Option 3: 20%
Option 4: 21%
Correct Answer: 21%
Solution :
Given: The radius of a circle is increased by 10%.
Let the radius be r units, then area = $\pi r^2$ sq. units
After a 10% increase, new radius = $(r+r×\frac{10}{100})=\frac{11r}{10}$ units
Now, the area = $\pi (\frac{11r}{10})^2=\frac{121\pi r^2}{100}$ sq. units
Therefore, the percentage increase in area is,
= $\frac{(\frac{121\pi r^2}{100}-\pi r^2)}{\pi r^2}×100$
= $(\frac{21\pi r^2}{100})×100$
= 21%
Hence, the correct answer is 21%.
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