Question

If the circumference of a circle is increased by $50\%$, by what percent will its area be increased?

• A. $75\%$
• B. $100\%$
• C. $125\%$
• D. $150\%$

Answer 1

Answer: (C)

$125\%$

Let initial radius be '$r$' and new radius be '$R$'

$\Rightarrow \frac{2\pi r}{2\pi R}=\frac{150}{100}\Rightarrow \frac{r}{R}=\frac{3}{2}$

$\therefore$ Ratio of area $=\frac{\pi r^2}{\pi R^2}={\left(\frac{3}{2}\right)}^2=\frac{9}{4}$

Increase in area $=\frac{9}{4}-1=\frac{5}{4}$

Therefore % increase in area $=\frac{\frac{5}{4}}{1}\times 100=125$%