Question

If a radius of a circle is increased by 5% then percentage increase in its area

Answer 1

let the original radius of circle be ' r '

original area :
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original area of circle = πr^2

if the radius is increased by 5 % then Find the new radius of circle .

new radius=r + 5%of r = r + 0.05r=1.05r

Find the new area :
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new area of circle = π ( 1.05r )^2

= 1.1025πr^2

Find the increase :

increase = new area - original area

= 1.1025πr^2 - πr^2 = πr^2 ( 1.1025 - 1 )

= 0.1025πr^2

Find the increase% :
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increase% = increase × 100/ original area

= 0.1025 πr^2 × 100 / πr^2

= 0.1025 × 100 = 10.25 %

therefore,

area of circle will be increased by 10.25 % .

short cut method :
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area of circle = πr^2

r^2 = r × r , let r = 5 , r = 5

increase in area = r + r + [( r × r )/ 100]

= 5 + 5 + [ ( 5 × 5 )/ 100 ]

= 10 + ( 25/ 100 ) = 10 + 0.25

= 10.25 %

Answer : 10.25 %

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