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Question
If the difference between the circumference and radius of a circle is 37 cm, then its area is
Options
154 cm2
160 cm2
200 cm2
150 cm2
Solution
We have given the difference between circumference and radius of the circle.
Let C be the circumference, r be the radius and A be the area of the circle.
Therefore, from the given condition we have
`C-r=2pir-r`
`∴ 37=2pir-r`
`∴37=r(2pi-1)`
`∴ r=37/((2pi-1))`
Now we will substitute `pi=22/7`
`∴ r= 37/((2xx22/7-1))`
`∴ r=37/((44/7-1))`
`∴ r=37/(((44-7)/7))`
`∴ r=37/((37/7))`
`∴ r=37xx7/37`
`∴ r=7`
Now we will substitute the value of r in`A=pir^2`.
`∴ A=pixx7^2`
Now we will substitute` pi=22/7`
`∴ A=22/7xx7^2`
`∴=22xx7`
`∴ A=154`
Therefore, area of the circle is `154 cm^2`
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