Question : If the radius of a circle is increased by 16%, its area increases by
Option 1: 34.56%
Option 2: 32%
Option 3: 16%
Option 4: 17.28%
Correct Answer: 34.56%
Solution :
Let the radius of the original circle = $r$
So, the Area of the original circle = $\pi r^2$
Radius of circle after 16% increase = $r+\frac{16r}{100} =1.16r$
Area of new circle = $\pi \times 1.16^2 = 1.3456r^2$
Percentage increase in area
$\frac{1.3456\pi r^2- \pi r^2}{\pi r ^2}\times 100$
= 34.56%
Hence, the correct answer is 34.56%.
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