If the circumference of a circle is increased by 50%, then

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If the circumference of a circle is increased by 50%, then its area will be increased by ?

1. 50%
2. 100%
3. 125%
4. 225%

Correct Option: C

Original circumference = 2πr
New circumference = (150 /100) x 2 πr
= 3πr

2πR = 3πr
⇒ R = 3r/2
Original area = πr²
New area = πR²
= π9r² / 4 = 9πr²/4

Increase in area = (9πr²/4 ) - (πr²)
= (5/4) πr²

Req. increase per cent = [{(5/4) πr²} / {πr²}] x 100
= 125 %