If the circumference of a circle is increased by 20%, what will be the effect on the circle ?

Solution(By Examveda Team)

Let the original circumference be x units.
Then,
New circumference = 120% of x = $$\left( {\frac{{6x}}{5}} \right)$$
Let original radius = r and new radius = R
$$\eqalign{ & 2\pi r = x \cr & \Rightarrow r = \frac{{7x}}{{2 \times 22}} \cr & \Rightarrow r = \frac{{7x}}{{44}} \cr} $$
And,
$$\eqalign{ & 2\pi R = \frac{{6x}}{5} \cr & \Rightarrow R = \frac{{6x}}{5} \times \frac{7}{{2 \times 22}} \cr & \Rightarrow R = \frac{{21x}}{{110}} \cr} $$
Original are :
$$\eqalign{ & = \pi {r^2} \cr & = \left( {\frac{{22}}{7} \times \frac{{7x}}{{44}} \times \frac{{7x}}{{44}}} \right) \cr & = \frac{{7{x^2}}}{{88}} \cr} $$
New area :
$$\eqalign{ & = \pi {R^2} \cr & = \left( {\frac{{22}}{7} \times \frac{{21x}}{{110}} \times \frac{{21x}}{{110}}} \right) \cr & = \frac{{63{x^2}}}{{550}} \cr} $$
Increase area :
$$\eqalign{ & = \left( {\frac{{63{x^2}}}{{550}} - \frac{{7{x^2}}}{{88}}} \right) \cr & = \frac{{77{x^2}}}{{2200}} \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{{77{x^2}}}{{2200}} \times \frac{{88}}{{7{x^2}}} \times 100} \right)\% \cr & = 44\% \cr} $$