Question : The radius of a circle is increased by 20%. Find the percentage increase in the circumference of the circle.
Option 1: 30%
Option 2: 20%
Option 3: 15%
Option 4: 40%
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Correct Answer: 20%
Solution :
Let the original radius be $r$.
New radius $=r+\frac{20}{100} \times =1.2r$
Old circumference $=2\pi r$
New circumference $=2 \pi \times 1.2r=2.4\pi r$
Increase in circumference $=2.4\pi r - 2 \pi r=0.4\pi r$
$\therefore$ Percentage increase in circumference $=\frac{0.4 \pi r}{2\pi r} \times 10=20\%$
Hence, the correct answer is 20%.
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