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A circular metal plate expands under heating so that its radiusincreases by 2%. Find  the approximateincrease in the area of the plate if the radius of the plate before heatingis 10cm.

Answer» `x=`radius & y= area
`y= pi x^2 `
`(/_x)/x xx 100 = 2`
`(/_ x)/10 xx 100 = 2`
`/_ x = 2/10= 0.2cm`
`dx= 0.2cm`
now,`y= pi x^2`
`dy/dx = 2x xx pi`
`dy/dx= 2 xx 10 xx pi = 20 pi`
`dy= 20 pi xx dx`
`dy= 20 xx pi xx 0.2= 4 pi`
`:. dy~= /_ y, so, /_ y= 4pi`
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