Question

If the circumference of a circle increases from $2\pi to4\pi$, then its area is:

• A. halved
• B. doubled
• C. tripled
• D. four times

Answer 1

The correct option is D four times

Circumference of a circle is given by $=2\pi \times radius$$=2\pi r$

If $r=1$, then circumference $=2\pi$ units

So, area $=\pi r^2=\pi (1{)}^2=\pi$ Units

New radius after increasing circumference:

$2\pi r=4\pi \Rightarrow r=2$

New area $=\pi r^2=\pi (2{)}^2=4\pi =4\times olderarea$

Hence, area becomes four times after increasing the circumference from $2\pi$ to $4\pi$.