Question

If the radius of a circle is increased by 3%, calculate the percentage increase in the area of the circle? (round off to 2 decimal places)

• A. 4.04%
• B. 8.16%
• C. 6.09%
• D. 10.25%

Answer 1

The correct option is C 6.09%

Let the initial radius of the circle be 'r'.
$\therefore \text{Initial Area =}𝛑r^2$

New radius = 103% of r

= $\frac{103}{100}r$

= $1.03r$

$\text{Final Area of circle =}𝛑(1.03r{)}^2$
= $1.0609𝛑r^2$


$\text{Percenatge change in area =}\frac{Finalarea-Initialarea}{Initialarea}\times 100\%$

= $\frac{1.0609𝛑r^2-𝛑r^2}{𝛑r^2}\times 100\%$

= $\frac{0.0609𝛑r^2}{𝛑r^2}\times 100\%$

= 6.09 %

∴ The percentage increase in area of the circle is 6.09%.