Question
If the radius of a circle is increased by 6% , then the area is increased by :
Answer: Option C
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Let the original radius be R cm. New radius = `(106/100 R) cm = ((53 R)/(50))cm`
Original area = ` pi R^2`
Increase in area = `pi ((53R)/(50))^2 - pi R^2` = `pi R^2[(53/50)^2 - 1]`
= `(pi R^2[(53)^2 - (50)^2])/(2500)` = `(piR^2(103 xx 3))/(2500) m^2`
Increase % = `((piR^2 xx 309)/(2500) xx (1)/(piR^2) xx 100)`% = 12.36 %
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