if the radius of a circle is decreased by 50 its..., Percentage, General Mathematics

Question:If the radius of a circle is decreased by `50%`, its area is reduced by :

A `25%` 
B `50%` 
C `75%` 
D None

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+ AnswerC

+ ExplanationLet original radius be R. Then, area` = π R^2` 

 New radius `= 50% of R = 50/100 R = R/2.`

New area`= π xx (R/2)^2`

`= (πR^2)/4`

decrease`= (πR^2 - (π R^2)/4)`

`= (3 π R^2)/4`

:. Decrease `% = ((3 πR^2)/(4) xx 1/(π R^2) xx 100)%`

`= 75%`.

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