Question

If the radius of a circle increased by 20% then the corresponding increase in the area of circle is ................

• A. 40%
• B. 44%
• C. 20%
• D. 21%

Answer 1

Answer: (B)

44%

Let the radius of original circle $=r$
$\therefore$ Area of original circle $=\pi r^2$
But, the radius of the circle is increased by $20\%$
$\therefore$ Radius of new circle $R=\frac{20r}{100}+r=1.2r$
Area of new circle $=\pi R^2$
$=\pi (1.2r{)}^2$
$=1.44\pi r^2$
Increased area $=1.44\pi r^2-\pi r^2$
$=0.44\pi r^2$
Percentage increase in area $=\frac{0.44\pi r^2}{\pi r^2}\times 100=44$%