Question

If the circumference of a circle is reduced by $50\%$ the area of the circle is reduced by:

• A. $25\%$
• B. $65\%$
• C. $50\%$
• D. $75\%$

Answer 1

The correct option is D $75\%$

If $r$ is the radius then circumference $=2\pi r$
if circumference is reduced to $\pi r$
$\Rightarrow$ Radius becomes $\frac{r}{2}$
$\Rightarrow Area=\frac{\pi r^2}{4}$
$\therefore$ Area is reduced by $\frac{3}{4}$th of the original area, i.e, by $75\%$