Question

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

Options

•  96%

• 40%

• 80%

• 48%

Answer 1

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%`