Question

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

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

Answer 1

The correct option is D $400\%$

Area of a circle$=\pi r^2$

Area of new circle$=\pi R^2$

Radius of new circle$=R=2r$

$\therefore$Area of new circle$=\pi {\left(2r\right)}^2=4\pi r^2$

Increase in area$=\frac{Areaofnewcircle}{Areaofcircle}\times 100\%$

$=\frac{4\pi r^2}{\pi r^2}\times 100\%$

$=400\%$