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The radius of a circle is increased so that its circumference increase by 5%. The area of the circle will increase by ?
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- 10 %
- 10.25 %
- 8.75 %
- 10.5 %
Correct Option: B
Let circumference = 100 cm .
Then, ∵ 2πr = 100
⇒ r = 100/2π
=50/π
⇒ New circumference
= 105 cm
Then, 2πR = 105
⇒ R = 105 / (2π)
&rArr Original area = [ π x (50/π) x (50/π) ]
= 2500/π cm2
⇒ New Area = [π x (105/2π) x (105/2π)]
= 11025 / (4π) cm2
⇒ Increase in area = [11025/(4π)] - 2500/π cm2
= 1025 / 4π cm2
Required increase percent [1025/(4π)] x 2500/π x 100 = 41/4%
= 10.25%
