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Question
If the circumference of a circle increases from 4π to 8π, then its area is
Options
halved
doubled
tripled
quadrupled
Solution
Let the circumference `C=4pi`
`∴ 2pi r=4pi`
`∴ r=2`
Therefore, area of the circle when radius of the circle is 2 can be calculated as below,
`pir^2=22/7xx4` .........(1)
Now when circumference is`C=8pi`, then the radius of the circle is calculated as below,
`∴ 2pi r=8pi`
`∴ r=4`
Therefore, area of the circle when radius of the circle is 2 can be calculated as below,
`pi r^2=22/7xx16`
`∴ pi r^2=4(22/7xx4)............(2)`
Therefore, from equation (1) and (2) we can say that its area is quadrupled
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