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प्रश्न
The area of a circle whose area and circumference are numerically equal, is
पर्याय
2 \[\pi\] sq. units
4 \[\pi\] units
6\[\pi\]sq. units
8 \[\pi\] sq. units
उत्तर
We have given that circumference and area of a circle are numerically equal.
Let it be x.
Let r be the radius of the circle, therefore, circumference of the circle is `2pi r^2`and area of the circle will bepir^2.
Therefore, from the given condition we have,
`2pir=x...............(1)`
`pir^2=x.............(2)`
Therefore, from equation (1)get r=x/2x. Now we will substitute this value in equation
(2) we get , `pi (x/2pi)^2=x`
Simplifying further we get,
`pi xx x^2/(4pi^2)=x`
Cancelling x we get,
`pixx x^2/(4pi^2)=x`
Now we will cancel` pi`
`x/4pi=1`...........(3)
Therefore, area of the circle is `4pi sq.unit`
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