Question

On increasing the diameter of a circle by 40%, its area will be increased by

(a) 40% (b) 80 % (c) 96 % (d) 82%

Answer 1

Correct option is C. $96\%$

Let the original radius of the circle be $r$.

Now, original area of the circle $=\pi r^2$

New radius of the circle $=r+40\%\times r=r+0.4r=1.4r$

New area of the circle $=\pi (1.4r{)}^2=1.96\pi r^2$

Increase in area $=1.96\pi r^2-\pi r^2=0.96\pi r^2$

Increase Percentage $=\frac{0.96\pi r^2}{\pi r^2}\times 100\%=96\%$