Question

If the radius of a circle is reduced to half, what happens to its area?

• A. The area reduces to half
• B. The area doubles
• C. The area reduces to one-fourth
• D. The area increases to four times

Answer 1

The correct option is C The area reduces to one-fourth

Initially, let the radius be 'r'. $Area=\pi r^2$
The radius is then reduced to $\frac{r}{2}$.
$Newarea=\pi \times {\left(\frac{r}{2}\right)}^2$
$=\frac{1}{4}\times \pi r^2$
The area reduces to one-fourth of its initial area.