Question

If the circumference of a circle is increased by $\frac{2}{5}$ calculate increase or decrease in area in percent.

Answer 1

Circumference of circle $2\pi r$ where $r$ is the radius of the circle.

So, Area of circle $=\pi r^2$

We know, Circumference is proportional to radius.

i.e., When circumference is increased by $\frac{2}{5}$ then the radius will also increased by $\frac{2}{5}$.

So, New radius $=\frac{2}{5}r$

And, New area $=\pi (\frac{2r}{5}{)}^2=\frac{4}{25}\pi r^2$

So, Increased in Area $=\frac{4}{25}\pi r^2-\pi r^2=-\frac{21}{25}\pi r^2$

$\therefore \%$ decrease in area $=\frac{\text{Decrease in Area}}{\text{Original Area}}\times 100$

$=\frac{\frac{21}{25}\pi r^2}{\pi r^2}\times 100$

$=84\%$