Question

If the radius of a circle is doubled then its area is increased by

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

Answer 1

The correct option is C $300\%$

Since, if radius of the circle = $r$
then Area of the circle = $\pi r^2$
if we doubled the radius then radius = $2r$
and Area of the circle = $\pi (2r{)}^2=4\pi r^2$
$\Rightarrow$ Increased Area = $4\pi r^2-\pi r^2=3\pi r^2$
% increase in area =$\frac{\text{increased area}}{\text{original area}}\times 100$%
$=\frac{3\pi r^2}{\pi r^2}\times 100$%
$=3\times 100$% = 300%
Option C is correct.