If diameter of a circle is increased by 40%, then its area increase by

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KollegeApply · Accepted Answer

If d is the original diameter of the circle, then the original radius is d/2 $\therefore$ area of the circle =pi (d/2)^2 $\therefore$ area of the circle=pixxd^$\frac{2}{4}$ If diameter of the circle increases by 40%, then new diameter of the circle is calculated as shown below, That is new diameter=d+04 d =1.4 d $\therefore$ new radius=(1.4 d)/2 $\therefore$ new radius=0.7 d So, new area will be pi(0.7 d)^2 $\therefore$ New radius=pixx0.49 d^2 Now we will calculate the change in area. $\therefore$ Change in area =pixx0.49d^2-pixxd^$\frac{2}{4}$ $\therefore$ change in area=(0.49-$\frac{1}{4}$)pid^2 $\therefore$ change in area=0.96 pi d^$\frac{2}{4}$ Therefore, its area is increased by 96%

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