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Question
If diameter of a circle is increased by 40%, then its area increase by
Options
96%
40%
80%
48%
Solution
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+04 d`
`=1.4 d`
∴ new radius=`(1.4 d)/2`
∴ new radius=`0.7 d`
So, new area will be` pi(0.7 d)^2`
∴ New radius=`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%`
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