if the circumference of a circle is increased by 50 then..., Area, General Mathematics

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

A 50% 
B 100% 
C 125% 
D 225%

/98

+ AnswerC

+ ExplanationLet original radius = r.

Then, circumference = 2 π r and area `= π r^2`

New circumference

`= (150/100 xx 2 π r)`

`= 3 π r`

Let radius now be R.

`2 π R = 3 π r => R = 3r/2.`

New area` = π R^2 = π ((9r^2)/4)`

            `= (9π r^2)/4`

Increase in area

`= ((9π r^2)/4 - π r^2)`

`= (5 π r^2)/4.`

:. Increase %` = ((5 π r^2)/4 xx 1/(π R^2) xx 100) %`

                 `= 125%`

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