Question

If the radius of a circle is increased by $10\%$ then what percent will increase the circumference of a circle?

• A. 10%
• B. 20%
• C. 110%
• D. 30%

Answer 1

The correct option is A 10%

$\text{Circumference of a circle}$

$=2\pi r$

$\text{Now, Radius increased by}10\%$

New Radius

$=r+10\%$ of $r$

$=r+\frac{10}{100}\times r$

$=\frac{11r}{10}$

New circumference

$=2\pi \times \frac{11r}{10}$

$=\frac{\pi \times 11\pi }{5}$

Change of circumference

$=2\pi r\times \frac{11}{10}-2\pi r$

$=\frac{2\pi r}{10}$

Increase percent in circumference

$=\frac{2\pi r}{10\times 2\pi r}\times 100\%$

$=10\%$