If d is the original diameter of the circle, then the original radius is`d/2`. ∴ area of the circle=`pi(d/2)^2` ∴ area of the circle=`pixxd^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+0.4d` `=1.4 d` ∴ new radius= `(1.4d)/2` ∴ new radius=`(1.4d)/2` ∴ new radius=`0.7 d` So, new area will be `pi(0.7 d).` ∴ new area=`pixx0.49 d^2` Now we will calculate the change in area. ∴ change in area = `pixx0.49d^2-pixxd^2/4` ∴ change in area=`(0.49-1/4)pid^2` ∴ change in area=`0.96 pi d^2/4` Therefore, its area is increased by `96%` |