Question : If the radius of a circle is increased by 10%, what will be the percentage increase in the area of the circle?
Option 1: 19
Option 2: 20
Option 3: 21
Option 4: 23
Correct Answer: 21
Solution :
Let the radius of the original circle = $r$
So, the area of the original circle = $\pi r^2$
Radius of circle after 10% increase = $r+\frac{10r}{100} =1.1r$
Area of new circle = $\pi \times 1.1^2 = 1.21r^2$
Percentage increase in area
= $\frac{1.21\pi r^2- \pi r^2}{\pi ^2}\times 100$
= 21%
Hence, the correct answer is 21.
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