Question

If the radius of a circle is increased by 10 % then corresponding increase in the area of the circle is .....$(\pi =3.14)$

• A. 19 %
• B. 10 %
• C. 21 %
• D. 20 %

Answer 1

Answer: (C)

21 %

Original radius $=$r

Original area $=\pi r^2$

New radius $=r+\frac{10}{100}r=\left(1.1\right)r$

New Area $=\pi (1.1r{)}^2$

$\%$ increase $=\frac{NewArea-Original}{OriginalArea}\times 100$

$\Rightarrow \frac{\pi \left(1.21r^2\right)-\pi r^2}{\pi r^2}\times 100$

$\Rightarrow \frac{\pi r^2[1.21-1]}{\pi r^2}\times 100$

$\Rightarrow 0.21\times 100=21\%$.