Question

If the radius of the circle is increased by $100\%$, then the area is increased by:

• A. $100\%$
• B. $200\%$
• C. $300\%$
• D. $400\%$

Answer 1

The correct option is C $300\%$

Let, radius of circle $=r$ and area $=A$.

We know that, $A_1=\pi .r^2$.

If radius increased by $100\%$,

then area,

$A_2=\pi {(r+r)}^2$ $=\pi {\left(2r\right)}^2$

$A_2=4\pi .r^2$.

Then, area is increased by:

$=\frac{(4\pi r^2-\pi r^2)\times 100}{\pi r^2}=\frac{\left(3\pi r^2\right)\times 100}{\pi r^2}$

$=\frac{3\times 100}{1}$ $=300\%$.

Hence, option $C$ is correct.