Question
If the radius of a circle is diminished by 10% , then its area is diminished by :
Answer: Option B
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Let the original radius be R cm.
New radius = (90% of R) cm = `(90/100 xx R) cm` = `(9R)/(10)` cm
Original area = `pi R^2`
Diminished area = `[pi R^2 - pi ((9R)/(10))^2] cm^2 = [(1 - 81/100) pi R^2]cm^2 `
= `(19/100 pi R^2) cm^2`
Decrease % = `((19 pi R^2)/(100) xx (1)/(pi R^2) xx 100)%` = 19%
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