Question

If the diameter of a circle is increased by 200% then its area is increased by

• A. 100%
• B. 200%
• C. 300%
• D. 800%

Answer 1

The correct option is D 800%

Let radius of circle is r

Then area of circle =$\pi r^2$

If radius increased 200% then radius =$\frac{300r}{100}=3r$

Then area of new circle =$\pi (9r{)}^2=9\pi r$

So increased in area =$9\pi r^2-\pi r^2=8\pi r^2$

% increased=$\frac{8\pi r^2}{\pi r^2}\times 100=800$%