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प्रश्न
On increasing the diameter of a circle by 40%, its area will be increased by
विकल्प
40%
80%
96%
82%
उत्तर
96%
Let d be the original diameter.
Radius `="d"/2`
Thus, we have;
Original area `= π xx ("d"/2)`
`= (pi"a"^2)/4`
New diameter = 140% of d
`= (140/100xx"d")`
`= (7"d")/5`
Now,
New radius ` =(7"d")/5xx2`
`=(7"d")/10`
New area `= pixx((7"d")/10)^2`
`=(49π"a""^2)/10`
Increase in the area`=((49pi"a"^2)/10 - (pi"a"^2)/4)``
`=(24π"a"^2)/100`
`=(6pi"a"^2)/25 `
We have ;
Increase in the area`=((6pi"a"^2)/25xx4/(pi"a"^2)xx100)%`
= 96 %
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